NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions

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# NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions

Edited By Ramraj Saini | Updated on Mar 01, 2024 06:44 PM IST

Direct and Inverse Proportions Class 8 Questions And Answers provided here. These NCERT Solutions are created by expert team at craeers360 keeping the latest syllabus and pattern of CBSE 2023-23. You must have come across many situations where changes in one quantity result in changes in other quantities. In mathematics, two quantities are said to be in proportional if the values of two quantities are related in such a way that changes in one results in a corresponding change in another quantity. You must have observed that when you increase the speed of the car it takes lesser time to cover the same distance. So speed is inversely proportional to time with a constant distance.

Practice all chapter of NCERT solutions for Class 8 Maths at here. Direct and Inverse Proportions class 8 solutions, you are going to deal with problems based on direct and indirect proportions. In this chapter, there are 2 exercises with 21 questions. All these questions are prepared in NCERT solutions for Class 8 Maths chapter 13 Direct and Inverse Proportions in a step-by-step manner. It will be very easy for you to understand the concept. There are solved examples, exercises, and daily life activities in the textbook for a better understanding of this chapter.

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## Direct and Inverse Proportions Class 8 Solutions - Important Points

• Proportions: Proportions are represented by the symbol ∝. For example, if p is proportional to q, it's denoted as p ∝ q. If p is inversely proportional to q, it's represented as "p ∝ 1/q." In both cases, the value of 'p' changes with 'q,' or when 'q' changes, 'p' changes. The proportionality constant represents the relationship between these values, and it indicates that two ratios, such as p/q and r/s, are equivalent, i.e., p/q = r/s.

• Direct Proportion or Variation: Two quantities, a and b, are in direct proportion if they change together in such a way that the ratio of their corresponding values remains constant. This is represented as a/b = k, where k is any positive number. For example, if the number of items bought increases, the total cost of purchase also increases.

• Inverse Proportion: Two quantities, x and y, are in inverse proportion if an increase in x leads to a proportional decrease in y (and vice versa) in a way that the product of their corresponding values remains constant. This is represented as xy = k. For example, if the number of people increases, the time taken to finish food decreases, or if the speed increases, the time required to cover a given distance decreases.

Free download NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions for CBSE Exam.

## Direct and Inverse Proportions Class 8 NCERT Solutions (Intext Questions and Exercise)

NCERT class 8 maths chapter 13 question answer - Topic 13.2 Direct Proportion

Answer:

If we want to know that they are directly proportional, then we calculate $\small \frac{x}{y}$ :

$\small \frac{x}{y}=\frac{20}{40} = \frac{17}{34}=\frac{14}{28}=\frac{11}{22}=\frac{8}{16}=\frac{5}{10}=\frac{2}{4}=\frac{1}{2}$ .

Hence we can say that x and y are directly proportional as $\small \frac{x}{y}$ cames out to be a constant equals $\small \frac{1}{2}$ .

Answer:

If x and y are directly proportional then $\frac{x}{y}$ must be equal to a constant value let say some 'k'.

Hence we then calculating: $\frac{x}{y}$

$\frac{6}{4}=\frac{3}{2}$ $\frac{10}{8}=\frac{5}{4}$ $\frac{14}{12}=\frac{7}{6}$ $\frac{18}{16}=\frac{9}{8}$

$\frac{22}{20}=\frac{11}{10}$ $\frac{26}{24}=\frac{13}{12}$ $\frac{30}{28}=\frac{15}{14}$ ,

as you can see that all these values are not equal hence,

we can say that x and y are not directly proportional.

Answer:

Calculating $\frac{x}{y}$ we get:

$\frac{5}{15}=\frac{1}{3}$ $\frac{8}{24}=\frac{1}{3}$ $\frac{12}{36}=\frac{1}{3}$

$\frac{15}{60}=\frac{1}{4}$ $\frac{18}{72}=\frac{1}{4}$

$\frac{20}{100}=\frac{1}{5}$

So, clearly $\frac{x}{y}$ equals to $\frac{1}{3},\frac{1}{4},\frac{1}{5}$ hence it is not equal to some constant value 'k'.

We can say that x and y are not directly proportional .

Answer:

Given that Principal (P) = 1000 and Rate (r) = 8% per annum(per year).

Calculating the Simple Interest:

The formula for the simple interest is = $\frac{P\times r\times t}{100}$ .

So, for 1 year :

$Simple Interest=\frac{P\times r\times t}{100}$ $=\frac{1000\times 8\times 1}{100}=80 rupees$ .

for 2 years :

$=\frac{1000\times 8\times 2}{100}=160 rupees$ .

similarly for 3 years:

$=\frac{1000\times 8\times 3}{100}=240 rupees$ .

Calculating the Compound Interest :

The formula for the compound interest is

$P(1+\frac{r}{100})^{t} - P$ .

So for 1 year :

$Compound Interest=P(1+\frac{r}{100})^{t} - P=1000(1+\frac{8}{100})^{1} - 1000$

$=1000(1+\frac{8}{100})^{1} - 1000=80rupees$ .

for 2 years :

$=1000(1+\frac{8}{100})^{2} - 1000=166.4rupees$ .

similarly for 3 years:

$=1000(1+\frac{8}{100})^{3} - 1000=259.71rupees$ .

Hence we have

 Time period 1 year 2 year 3 year Simple Interest(in rupees) 80 160 240 Compound Interest(in rupees) 80 166.4 259.71

In case of simple interest

$\frac{80}{1}=\frac{160}{2}=\frac{240}{3}=80 \ gives \ the \ same \ value \ 80.$

Simple interest is directly proportional with time.

While in case of compound interest:

$\frac{80}{1}\neq \frac{166.4}{2}\neq\frac{259.71}{3}$ does not give the same constant.

Compound interest is not directly proportional with time.

Class 8 direct and inverse proportions NCERT solutions - Exercise: 13.1

Answer:

We say that x and y are in direct proportion, if $\frac{x}{y}=k$ or $x = ky.$

Hence in the given problem we have,

Charges for the parking :

 y x 4 hours Rs. 60 8 hours Rs. 100 12 hours Rs. 140 24 hours Rs. 180

considering x to be charged to be paid and y to be the parking time.

Then we calculate $\frac{x}{y}$ ,

For:- 4 hours: $\frac{60}{4}=\frac{15}{1}$ 8 hours : $\frac{100}{8}=\frac{25}{2}$

12 hours : $\frac{140}{12}=\frac{35}{3}$ 24 hours: $\frac{180}{24}=\frac{15}{2}$

Clearly $\frac{x}{y}$ is not equal to some constant 'k', then we can say that

Parking charges are not in direct proportion to parking time.

Answer:

Suppose the parts of red pigment is x and parts of base, is ' y '.

As the requirement of the number of parts of base for 1 part of red pigment is 8,

and as the parts of red pigment is increases, parts of the base also increase in the same ratio. It is a case of direct proportion.

we can assume other parts of the base that will be required for red pigments as y1, y2, y3 and y4 for parts of pigment 4, 7, 12 and 20 respectively.

We make use of the relation of type $\frac{1}{8}=\frac{4}{y1}$

That gives for the (i) case $y1\times 1=8\times 4$ or $y1=32$ .

32 parts of the base will be required for the 4 parts of the red pigment.

(ii) If parts of red pigment used is 7 then parts of base used will be $\frac{1}{8}=\frac{7}{y2}$

that gives $y2\times 1=8\times 7$ or $y2= 56$ .

56 parts of the base will be required for the 7 parts of the red pigment.

(iii) for 12 parts of red pigment : $\frac{1}{8}=\frac{12}{y3}$

we have $y3\times 1 = 8\times 12$ or $y3=96$ .

so, 96 parts of the base will be required for the 12 parts of the red pigment.

(iv) for 20 parts of red pigment: $\frac{1}{8}=\frac{20}{y4}$

we have $y4\times 1 = 8\times 20$ or $y4 = 160$ .

Hence for the following parts of red pigment, parts of base are given :

 Parts of red pigment 1 4 7 12 20 Parts of base 8 32 56 96 160

Answer:

As we know that mL of red pigment is directly proportional to the mL of base.

We have to calculate for the mL of red pigment used when we mix 1800mL of base,

So, for 1 part of red pigment requires 75mL of base, then we

$\frac{redpigment(mL)}{base(mL)}= \frac{1}{75}$ .

So for 1800mL of the base, mL of the red pigment should be mixed

$\frac{redpigment(mL)}{1800mL}= \frac{1}{75}$ or $redpigment(mL)=\frac{1800mL}{75}=24mL$

Hence for the 1800mL of base, we will mix 24 parts of red pigment .

Answer:

Given that a machine is capable of filling 840 bottles in 6 hours. So, we can say that it is directly proportional to the time.

we can assume that bottles it will fill in five hours would be ' x '

So we got the relation; $\frac{840}{6}=\frac{x}{5}$ ,

solving for x we will get $840\times 5 = 6\times x$ or $x= \frac{840\times 5}{6}= 700$ .

Machine will fill 700 bottles in 5 hours .

Answer:

We can calculate it easily,

Given that for 50,000 times enlarged, the photograph of a bacteria attains a length of 5cm.

So, we have to calculate the actual length of the bacteria(assume it to be ' x 'cm) that is when the photograph is enlarged to 1 time

Knowing that the microscope's zoom has a direct relation with the length of bacteria observed So, we get the relation ;

$\frac{50,000}{1}=\frac{5cm}{x}$

Solving the equation for x we get;

$x=\frac{5cm}{50,000}=1\times 10^{-4}cm$

The actual length of the bacteria is $10^{-4}cm$ which is so small to be observed through naked eyes.

Now, calculating the length of bacteria when it the photograph is enlarged 20,000 times,

assume it as ' y '.

So, we get this relation

$\frac{20,000}{50,000}=\frac{y}{5cm}$

solving for y we get;

$y=\frac{20,000\times 5cm}{50,000} = 2cm$ .

So, if the photograph is enlarged 20,000 times only then the enlarged length would be 2cm.

Answer:

Given that the mast of the model ship is 9 m high, while the mast of the actual ship is 12 m.

If the length of the ship given is 28m then,

Length of the model ship can be obtained from the direct proportion relation of mast height and length of ship.

We obtained the relation:

$\frac{height\ of\ mast(model)}{height\ of\ mast (actual)} = \frac{length\ of\ ship(model)}{length\ of\ ship(actual)}$

So, by the relation we have;

Let us assume that the length of model ship is ' x '

$\frac{9cm}{1200cm} = \frac{x}{2800cm}$ $\because (1m = 100cm)$

after solving this relation we get,

$x=\frac{9cm\times 2800cm}{1200cm}= 21cm$ ,

Length of the model ship is 21cm.

Answer:

Here given that 2 kg of sugar contains $9\times 10^6$ crystals.

So, we have to find the number of crystals in 5 kg of sugar as well as in 1.2 kg of sugar:

As here we will assume that all crystals have the same dimensions i.e., length, breadth, and width. Then the weight of sugar follows the direct proportion with the number of crystals as increasing the number of crystals there will be an increase in the weight also.

(i) For 5 kg sugar:

let the number of crystals be 'x' then,

we have the relation:

$\frac{5kg}{2kg}=\frac{x}{9\times 10^6}$ , calculating x from this relation,

$x=\frac{5kg\times 9\times 10^6}{2kg}=22.5\times 10^6$ .

Therefore 5 kg of sugar contains $22.5\times 10^6$ sugar crystals.

(ii) For 1.2 kg sugar:

Let the number of cystals be 'y' then,

we have the relation:

$\frac{1.2kg}{2kg}=\frac{y}{9\times 10^6}$ . calculating similarly for y we get

$y=5.4\times 10^6$ .

Therefore 1.2 kg of sugar contains $5.4\times 10^6$ sugar crystals.

Answer:

Given that Rashmi has a road map with a scale of 1cm representing 18km.

So we have a direct relation of scale distance and distance driven in the road.

For 72 km she drove on a road, Distance covered in the map would be 'x' cm

$\frac{1cm}{18km}=\frac{x}{72km}$ ,

$x=\frac{72}{18}cm\ or \ x=4cm$ .

Hence, For 72km driven in the road, we have to move a distance of 4cm on the map.

(i) the length of the shadow cast by another pole 10 m 50 cm high

(ii) the height of a pole which casts a shadow 5m long.

Answer:

Consider there is a direct proportion relation of pole height with pole shadow.

So we have 5m 60cm high verticle pole that casts a shadow of 3m 20cm long .

hence,

(i) for the length of the shadow cast by another pole of 10 m 50cm high would be ' x ' cm;

$\frac{560cm}{320cm}=\frac{1050cm}{x}$

finding x from the equation we get;

$x=600cm$ .

Therefore for a 10m 50cm pole we would get a shadow of 600cm or 6m length.

(ii) The height of a pole which casts a shadow of 5m long let it be 'y'

similar relation holds here also, so we can apply it once more

$\frac{560cm}{320cm}=\frac{y}{500cm}$ ,

we get $y=875cm\ or\ 8m\ 75cm$ .

Thus, the height of a pole which casts a shadow of 5m long is 8m 75cm.

Answer:

If the speed of the truck remains the same, then we can say that the distance travelled by the truck is directly proportional to the time.

After taking 5 hours the truck will travel a distance of let say ' x ';

Hence we obtain the relation:

$\frac{14km}{25minutes}=\frac{x}{5\times60minutes }$

$x=\frac{14km\times 5\times60minutes}{25minutes}=168km$ ;

thus the truck would travel a distance of 168km in 5 hours.

Class 8 maths chapter 13 NCERT solutions - topic 13.3 inverse proportion

Answer:

Finding if x and y are in inverse proportion:

Two quantities x and y are said to vary in inverse proportion, if there exists a relation of the type xy = k between them, k being a constant

so, calculating xy for each case,

we have

$50\times 5 = 250$ $40\times 6 = 240$ $30\times 7 = 210$ $20\times 8 = 160$ ,

clearly xy is not equal to a constant value 'k',

hence x and y are not inversely proportional.

Answer:

Finding if x and y are in inverse proportion:

Two quantities x and y are said to vary in inverse proportion, if there exists a relation of the type xy = k between them, k being a constant

so, calculating xy for each case,

we have

$100\times 60 = 6000$ $200\times 30 = 6000$ $300\times 20 = 6000$ $400\times 15 = 6000$ ,

clearly xy is equal to a constant value 'k=6000',

hence x and y are inversely proportional.

Answer:

Finding if x and y are in inverse proportion:

Two quantities x and y are said to vary in inverse proportion, if there exists a relation of the type xy = k between them, k being a constant

so, calculating xy for each case,

we have

$90\times 10 = 900$ $60\times 15 = 900$ $45\times 20 = 900$ $30\times 25 = 750$ $20\times 30 = 600$ $5\times 35 = 175$

clearly xy is not equal to a constant value 'k',

hence x and y are not inversely proportional.

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions - Exercise: 13.2

(i) The number of workers on a job and the time to complete the job.

(ii) The time taken for a journey and the distance travelled in a uniform speed.

(iii) Area of cultivated land and the crop harvested.

(iv) The time taken for a fixed journey and the speed of the vehicle.

(v) The population of a country and the area of land per person.

Answer:

(i) As the number of workers on a job increases the time taken to complete the job decreases, hence it is an inverse proportion .

(ii) Distance and time are directly proportional to each other as time increases you could travel more distance compared to if you get less time to travel. Hence it is not an inverse proportion.

(iii) Both area of cultivated land and crop arvested are directly proportional, more the area cultivated more crop harvest. Hence it is not an inverse proportion.

(iv) With more speed if you are travelling lesser the time taken for a fixed journey to complete. Hence it is an inverse proportion.

(v) The population of a country if increases then there would be lesser area available per person, Hence it is an inverse proportion.

 Number of winners 1 2 4 5 8 10 20 Prize for each winner (in Rs.) 1,00,000 50,000 .... .... .... .... ....

Answer:

Let us assume that for the number of winners 4, 5, 8, 10 and 20 are x1, x2, x3, x4, and x5 respectively and given that the prize money of Rs. 1,00,000 is to be divided equally amongst the winners.

Thus we have,

For 4 number of winners:

$\frac{Rs.1,00,000}{4}=Rs.25,000$

So Rs. 25,000 to be distributed among each.

For 5 number of winners:

$\frac{Rs.1,00,000}{5}=Rs.20,000$

So Rs. 20,000to be distributed among each.

For 8 number of winners:

$\frac{Rs.1,00,000}{8}=Rs.12,500$

So Rs. 12,500 to be distributed among each.

For 10 number of winners:

$\frac{Rs.1,00,000}{10}=Rs.10,000$

So Rs. 10,000 each would get.

similarly for 20 number of winners:

$\frac{Rs.1,00,000}{20}=Rs.5,000$

So Rs. 5000 each would get.

Hence we have;

 Number of winners (x) 1 2 4 5 8 10 20 Prize for each winner (in ? ) (y) 1,00,000 50,000 25,000 20,000 12,500 10,000 5,000

Two quantities x and y are said to be in inverse proportional if they satisfy the given relation;

xy=k; where k is a constant.

Calculating xy:

$xy=1\times1,00,000=2\times50,000=4\times25,000=5\times20,000=8\times12,500=10\times10,000=20\times5,000=1,00,000$

Clearly, we can see that the prize money given to an individual winner is inversely proportional.

Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?

 Number of spokes 4 6 8 10 12 Angle between a pair of consecutive .... .... ....

Answer:

(i) Calculating the angle formed when using a different number of spokes:

The angle formed when using 8, 10, and 12 number of spokes a1,a2, and a3 respectively.

Hence, we have

For 8 number of spokes:

$\frac{360^{\circ}}{8} = 45^{\circ}$

For 10 number of spokes:

$\frac{360^{\circ}}{10} = 36^{\circ}$

For 12 number of spokes:

$\frac{360^{\circ}}{12} = 30^{\circ}$

 Number of spokes (x) 4 6 8 10 12 Angle between a pair of consecutive spokes (y) 90° 60° 45° 36° 30°

Calculating xy:

$4\times90^{\circ} = 6\times60^{\circ} = 8\times45^{\circ}=10\times36^{\circ}=12\times30^{\circ}=360^{\circ}$

Hence we say that the number of spokes (x) and the angle formed (y) between them are inverse proportion to each other.

 Number of spokes (x) 4 6 8 10 12 Angle between a pair of consecutive spokes (y) 90° 60° 45° 36° 30°

Answer:

The angle between a pair of consecutive spokes on a wheel with 15 spokes is calculated as:

as we know the constant value k=360 then we can easily calculate the angle for 15 spokes:

$\frac{360^{\circ}}{15}=24^{\circ}$

Hence angle made is 24 degrees .

How many spokes would be needed, if the angle between a pair of consecutive spokes is $40^{\circ}$ ?

 Number of spokes (x) 4 6 8 10 12 Angle between a pair of consecutive spokes (y) 90° 60° 45° 36° 30°

Answer:

If the angle between a pair of consecutive spokes is $40^{\circ}$ then,

Number of spokes needed would be $\frac{360^{\circ}}{40^{\circ}}=9$

Hence the required number of spokes for having 40 degrees of angle is 9

Answer:

Given that the box of sweets is divided among 24 children, getting 5 sweets each.

If the number of children is reduced by 4 then the number of children now is $24-4=20$ .

As here if the number of children increases then the number of sweets they will get decreases hence we can say that there exists an inverse relationship between them.

Hence,

if we assume:

Number of children before (x1) = 24

Number of sweets each would get before (y1) = 5

and number of children after reduction (x2) = 20

and the number of sweets each would get after reduction is y2

Then the relation holds;

$x1\times y1=x2\times y2$

or $24\times 5=20\times y2$ or $y2= 6$ .

Hence each child will get 6 number of sweets .

Answer:

The farmer has 20 animals to feed for 6 days and after that farmer added 10 more animals to feed that counts to ( 20+10 = 30 ). So, assume that food will now long last to ' x ' days.

As the number of animals increases the required food increases but the day up to which the food will long last decreases.

Hence there exist an inverse proportion between the number of days and the number of animals.

So, we can write the relation as:

$20\times 6 = 30\times x$ or $x= 4$ days.

The food will last for about 4 days if 30 animals are there.

Answer:

Here the situation is given that a contractor estimates that 3 persons could rewire Jasminder's house in 4 days.

Now, as the number of person increases the time they take to complete the job will decrease .

Hence there is an inverse relationship among the number of persons and the time they took.

Jasminer now uses 4 persons instead of 3, then we can assume the time 4 persons will take be ' x '

So, we can write the relation as:

$3\times 4days = 4\times xdays$ . or $x= 3 days$ .

Thus, the 4 persons complete the job in 3 days.

We can easily calculate the required number of boxes to be filled, let us assume it to be 'x'

Given that a batch of bottles were packed in 25 boxes with 12 bottles in each box, Hence the total number of bottles will be $= 25\times 12 = 300$ .

So, as they produced the same number of bottles every batch and as the number of boxes increases, the bottles in each box decrease.

Hence there holds an inverse relation here,

$25\times 12 = 20\times x$ or $x=15$ boxes.

If the batch is packed using 20 bottles in each box then 15 boxes would be filled.

Answer:

Given that a factory requires 42 machines to produce a given number of articles in 63 days .

Then we know that as the number of machines increases the time taken to produce a given number of articles decreases. Hence there holds an inverse relation here,

And let the number of machines required to produce the same number of articles in 54 days be 'x'.

Then the relation;

$42\times 63days = x\times 54days$ or $x = 49$ .

Hence 49 machines would be required to produce the articles in 54 days.

Answer:

Given that a car has a speed of 60 km/h which is travelling to a destination and takes 2 hours to complete it.

Speed and time are inversely related to each other.

Assume the time it would take when travelling at 80km/h be 'x'

Therefore we can write the equation when the car travels at the speed of 80 km/h as:

$2hours\times 60km/h = x\times 80km/h$

or $x= 1.5 hours$ or $1 hour\ and\ 30 minutes.$

Question:10(i) Two persons could fit new windows in a house in 3 days.

One of the persons fell ill before the work started. How long would the job take now?

Answer:

Here, given that 2 persons could fit new windows in a house in 3 days.

(i) 1 person has fallen ill so, now the number of persons remaining is only one. Assume that the only person which is working takes the time of 'x' days.

hence we could write the inverse relation as;

$2persons\times 3 days = 1 person\times x days$

or $x= 6days$ .

One person will take 6 days to complete that window job.

Question:10(ii) Two persons could fit new windows in a house in 3 days.

How many persons would be needed to fit the windows in one day?

Answer:

(ii) So, now we are calculating the number of persons that would be needed to fit the windows in one day. Let it be 'y'.

So from previous part (i) we have the relation; $2 persons\times 3 days = y\ persons\times 1 day$ .

or $y = 6\ persons$ .

hence the required number of persons would be 6.

Answer:

Given :

A school has 8 periods a day each of 45 minutes duration.

So, if the school hours of school is fixed then there exists an inverse relationship between each period duration and the number of periods.

We can take the time of each period to be 't' if the school has 9 periods a day.

Hence we can write the relation as;

$8\times 45minutes = 9\times t\ minutes$ or $t = 40 minutes$ .

The time of each period would be 40 minutes when 9 periods are there in one day.

## Direct and inverse proportions class 8 NCERT solutions - Topics

• Direct Proportion
• Inverse Proportion

What is a Direct Proportion?

Two quantities 'a' and 'b' are said to be in direct proportion if the increase (decrease) in 'a' results in the increase (decrease) in 'b' in such a manner that the ratio of their corresponding values remains constant. That is if a/b= k

What is Inverse Proportional?

Two values are Inversely proportional it means decreases in one value results in a gradual increase in other value. Example- If the distance is fixed, speed and time are inversely proportional to each other.

$Speed=\frac{Distance}{Time}$

$Speed \propto \frac{Distance}{Time}$ ( If Distance is fixed)

## NCERT Solutions for Class 8 Maths - Chapter Wise

 Chapter -1 Rational Numbers Chapter -2 Linear Equations in One Variable Chapter-3 Understanding Quadrilaterals Chapter-4 Practical Geometry Chapter-5 Data Handling Chapter-6 Squares and Square Roots Chapter-7 Cubes and Cube Roots Chapter-8 Comparing Quantities Chapter-9 Algebraic Expressions and Identities Chapter-10 Visualizing Solid Shapes Chapter-11 Mensuration Chapter-12 Exponents and Powers Chapter-13 Direct and Inverse Proportions Chapter-14 Factorization Chapter-15 Introduction to Graphs Chapter-16 Playing with Numbers

## Key Features Of Direct And Inverse Proportions Class 8 Solutions

Complete Coverage: Maths chapter 13 class 8 solutions cover all topics and concepts related to direct and inverse proportions as per the Class 8 syllabus.

Step-by-Step Solutions: Class 8 maths ch 13 question answer are detailed, step-by-step explanations for each problem, making it easy for students to understand and apply mathematical concepts related to direct and inverse proportions.

Clarity of Concepts: Focusing on clarifying the fundamental properties and principles related to direct and inverse proportions, including proportionality constants and the concept of inverse variation.

## NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions - Benefits

• You will also know different ways to solve the problems.
• You will also get solutions to the practice questions given below every topic which will give you conceptual clarity.
• You will also get some short tricks and tips to solve some specific problems.
• In these class 8 maths ch 13 question answers, you will learn to calculate simple and compound interest which may be useful in real life too.
• It is going to help you with your homework as all the practice questions including questions given below every topic are covered in this article.

## NCERT Books and NCERT Syllabus

### Frequently Asked Question (FAQs)

1. What are the important topics of chapter Direct and Inverse Proportions ?

The basic concept of direct and inverse proportions, properties, and real-life applications of direct and inverse proportions are the important topics of this chapter. students can practice problems of ch 13 maths class 8 to command the concepts.

2. Does CBSE class maths is tough ?

CBSE class 8 maths is a basic and very simple maths where most of the topics related to the previous classes.

3. Which is the official website of NCERT ?

NCERT official is the official website of the NCERT where you can get NCERT textbooks and syllabus from class 1 to 12.

4. Does CBSE provide NCERT solutions for class 8 ?

CBSE doesn't provide NCERT solutions for any class or subject.

5. Where can I find the complete solutions of NCERT for class 8 ?

Here you will get the detailed NCERT solutions for class 8 by clicking on the link.

6. Where can I find the complete solutions of NCERT for class 8 maths ?

Here you will get the detailed NCERT solutions for class 8 maths by clicking on the link.

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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

 Option 1) Option 2) Option 3) Option 4)

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

 Option 1) 2.45×10−3 kg Option 2)  6.45×10−3 kg Option 3)  9.89×10−3 kg Option 4) 12.89×10−3 kg

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

 Option 1) Option 2) Option 3) Option 4)

A particle is projected at 600   to the horizontal with a kinetic energy . The kinetic energy at the highest point

 Option 1) Option 2) Option 3) Option 4)

In the reaction,

 Option 1)   at STP  is produced for every mole   consumed Option 2)   is consumed for ever      produced Option 3) is produced regardless of temperature and pressure for every mole Al that reacts Option 4) at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, will contain 0.25 mole of oxygen atoms?

 Option 1) 0.02 Option 2) 3.125 × 10-2 Option 3) 1.25 × 10-2 Option 4) 2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

 Option 1) decrease twice Option 2) increase two fold Option 3) remain unchanged Option 4) be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

 Option 1) Molality Option 2) Weight fraction of solute Option 3) Fraction of solute present in water Option 4) Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

 Option 1) twice that in 60 g carbon Option 2) 6.023 × 1022 Option 3) half that in 8 g He Option 4) 558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

 Option 1) less than 3 Option 2) more than 3 but less than 6 Option 3) more than 6 but less than 9 Option 4) more than 9
##### Data Administrator

Database professionals use software to store and organise data such as financial information, and customer shipping records. Individuals who opt for a career as data administrators ensure that data is available for users and secured from unauthorised sales. DB administrators may work in various types of industries. It may involve computer systems design, service firms, insurance companies, banks and hospitals.

4 Jobs Available
##### Bio Medical Engineer

The field of biomedical engineering opens up a universe of expert chances. An Individual in the biomedical engineering career path work in the field of engineering as well as medicine, in order to find out solutions to common problems of the two fields. The biomedical engineering job opportunities are to collaborate with doctors and researchers to develop medical systems, equipment, or devices that can solve clinical problems. Here we will be discussing jobs after biomedical engineering, how to get a job in biomedical engineering, biomedical engineering scope, and salary.

4 Jobs Available
##### Ethical Hacker

A career as ethical hacker involves various challenges and provides lucrative opportunities in the digital era where every giant business and startup owns its cyberspace on the world wide web. Individuals in the ethical hacker career path try to find the vulnerabilities in the cyber system to get its authority. If he or she succeeds in it then he or she gets its illegal authority. Individuals in the ethical hacker career path then steal information or delete the file that could affect the business, functioning, or services of the organization.

3 Jobs Available
##### GIS Expert

GIS officer work on various GIS software to conduct a study and gather spatial and non-spatial information. GIS experts update the GIS data and maintain it. The databases include aerial or satellite imagery, latitudinal and longitudinal coordinates, and manually digitized images of maps. In a career as GIS expert, one is responsible for creating online and mobile maps.

3 Jobs Available
##### Data Analyst

The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.

Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.

3 Jobs Available
##### Geothermal Engineer

Individuals who opt for a career as geothermal engineers are the professionals involved in the processing of geothermal energy. The responsibilities of geothermal engineers may vary depending on the workplace location. Those who work in fields design facilities to process and distribute geothermal energy. They oversee the functioning of machinery used in the field.

3 Jobs Available
##### Database Architect

If you are intrigued by the programming world and are interested in developing communications networks then a career as database architect may be a good option for you. Data architect roles and responsibilities include building design models for data communication networks. Wide Area Networks (WANs), local area networks (LANs), and intranets are included in the database networks. It is expected that database architects will have in-depth knowledge of a company's business to develop a network to fulfil the requirements of the organisation. Stay tuned as we look at the larger picture and give you more information on what is db architecture, why you should pursue database architecture, what to expect from such a degree and what your job opportunities will be after graduation. Here, we will be discussing how to become a data architect. Students can visit NIT Trichy, IIT Kharagpur, JMI New Delhi

3 Jobs Available
##### Remote Sensing Technician

Individuals who opt for a career as a remote sensing technician possess unique personalities. Remote sensing analysts seem to be rational human beings, they are strong, independent, persistent, sincere, realistic and resourceful. Some of them are analytical as well, which means they are intelligent, introspective and inquisitive.

Remote sensing scientists use remote sensing technology to support scientists in fields such as community planning, flight planning or the management of natural resources. Analysing data collected from aircraft, satellites or ground-based platforms using statistical analysis software, image analysis software or Geographic Information Systems (GIS) is a significant part of their work. Do you want to learn how to become remote sensing technician? There's no need to be concerned; we've devised a simple remote sensing technician career path for you. Scroll through the pages and read.

3 Jobs Available
##### Budget Analyst

Budget analysis, in a nutshell, entails thoroughly analyzing the details of a financial budget. The budget analysis aims to better understand and manage revenue. Budget analysts assist in the achievement of financial targets, the preservation of profitability, and the pursuit of long-term growth for a business. Budget analysts generally have a bachelor's degree in accounting, finance, economics, or a closely related field. Knowledge of Financial Management is of prime importance in this career.

4 Jobs Available
##### Data Analyst

The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.

Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.

3 Jobs Available
##### Underwriter

An underwriter is a person who assesses and evaluates the risk of insurance in his or her field like mortgage, loan, health policy, investment, and so on and so forth. The underwriter career path does involve risks as analysing the risks means finding out if there is a way for the insurance underwriter jobs to recover the money from its clients. If the risk turns out to be too much for the company then in the future it is an underwriter who will be held accountable for it. Therefore, one must carry out his or her job with a lot of attention and diligence.

3 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### Operations Manager

Individuals in the operations manager jobs are responsible for ensuring the efficiency of each department to acquire its optimal goal. They plan the use of resources and distribution of materials. The operations manager's job description includes managing budgets, negotiating contracts, and performing administrative tasks.

3 Jobs Available
##### Stock Analyst

Individuals who opt for a career as a stock analyst examine the company's investments makes decisions and keep track of financial securities. The nature of such investments will differ from one business to the next. Individuals in the stock analyst career use data mining to forecast a company's profits and revenues, advise clients on whether to buy or sell, participate in seminars, and discussing financial matters with executives and evaluate annual reports.

2 Jobs Available
##### Researcher

A Researcher is a professional who is responsible for collecting data and information by reviewing the literature and conducting experiments and surveys. He or she uses various methodological processes to provide accurate data and information that is utilised by academicians and other industry professionals. Here, we will discuss what is a researcher, the researcher's salary, types of researchers.

2 Jobs Available
##### Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.

5 Jobs Available
##### Transportation Planner

A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.

3 Jobs Available
##### Environmental Engineer

Individuals who opt for a career as an environmental engineer are construction professionals who utilise the skills and knowledge of biology, soil science, chemistry and the concept of engineering to design and develop projects that serve as solutions to various environmental problems.

2 Jobs Available
##### Safety Manager

A Safety Manager is a professional responsible for employee’s safety at work. He or she plans, implements and oversees the company’s employee safety. A Safety Manager ensures compliance and adherence to Occupational Health and Safety (OHS) guidelines.

2 Jobs Available
##### Conservation Architect

A Conservation Architect is a professional responsible for conserving and restoring buildings or monuments having a historic value. He or she applies techniques to document and stabilise the object’s state without any further damage. A Conservation Architect restores the monuments and heritage buildings to bring them back to their original state.

2 Jobs Available
##### Structural Engineer

A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software.

2 Jobs Available
##### Highway Engineer

Highway Engineer Job Description: A Highway Engineer is a civil engineer who specialises in planning and building thousands of miles of roads that support connectivity and allow transportation across the country. He or she ensures that traffic management schemes are effectively planned concerning economic sustainability and successful implementation.

2 Jobs Available
##### Field Surveyor

Are you searching for a Field Surveyor Job Description? A Field Surveyor is a professional responsible for conducting field surveys for various places or geographical conditions. He or she collects the required data and information as per the instructions given by senior officials.

2 Jobs Available
##### Orthotist and Prosthetist

Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.

6 Jobs Available
##### Pathologist

A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.

5 Jobs Available
##### Gynaecologist

Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth.

4 Jobs Available
##### Audiologist

The audiologist career involves audiology professionals who are responsible to treat hearing loss and proactively preventing the relevant damage. Individuals who opt for a career as an audiologist use various testing strategies with the aim to determine if someone has a normal sensitivity to sounds or not. After the identification of hearing loss, a hearing doctor is required to determine which sections of the hearing are affected, to what extent they are affected, and where the wound causing the hearing loss is found. As soon as the hearing loss is identified, the patients are provided with recommendations for interventions and rehabilitation such as hearing aids, cochlear implants, and appropriate medical referrals. While audiology is a branch of science that studies and researches hearing, balance, and related disorders.

3 Jobs Available
##### Oncologist

An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.

3 Jobs Available
##### Anatomist

Are you searching for an ‘Anatomist job description’? An Anatomist is a research professional who applies the laws of biological science to determine the ability of bodies of various living organisms including animals and humans to regenerate the damaged or destroyed organs. If you want to know what does an anatomist do, then read the entire article, where we will answer all your questions.

2 Jobs Available
##### Actor

For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs.

4 Jobs Available
##### Acrobat

Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.

3 Jobs Available
##### Video Game Designer

Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages.

Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.

3 Jobs Available
##### Radio Jockey

Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

3 Jobs Available
##### Choreographer

The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.

2 Jobs Available
##### Social Media Manager

A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.

2 Jobs Available
##### Photographer

Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.

2 Jobs Available
##### Producer

An individual who is pursuing a career as a producer is responsible for managing the business aspects of production. They are involved in each aspect of production from its inception to deception. Famous movie producers review the script, recommend changes and visualise the story.

They are responsible for overseeing the finance involved in the project and distributing the film for broadcasting on various platforms. A career as a producer is quite fulfilling as well as exhaustive in terms of playing different roles in order for a production to be successful. Famous movie producers are responsible for hiring creative and technical personnel on contract basis.

2 Jobs Available
##### Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.

5 Jobs Available
##### Vlogger

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion.

Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article.

3 Jobs Available
##### Publisher

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

3 Jobs Available
##### Journalist

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

3 Jobs Available
##### Editor

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

3 Jobs Available
##### Reporter

Individuals who opt for a career as a reporter may often be at work on national holidays and festivities. He or she pitches various story ideas and covers news stories in risky situations. Students can pursue a BMC (Bachelor of Mass Communication), B.M.M. (Bachelor of Mass Media), or MAJMC (MA in Journalism and Mass Communication) to become a reporter. While we sit at home reporters travel to locations to collect information that carries a news value.

2 Jobs Available
##### Corporate Executive

Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.

2 Jobs Available
##### Multimedia Specialist

A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications.

2 Jobs Available
##### Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.

5 Jobs Available
##### Quality Controller

A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.

A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

3 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### QA Lead

A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans.

2 Jobs Available
##### Structural Engineer

A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software.

2 Jobs Available
##### Process Development Engineer

The Process Development Engineers design, implement, manufacture, mine, and other production systems using technical knowledge and expertise in the industry. They use computer modeling software to test technologies and machinery. An individual who is opting career as Process Development Engineer is responsible for developing cost-effective and efficient processes. They also monitor the production process and ensure it functions smoothly and efficiently.

2 Jobs Available
##### AWS Solution Architect

An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party.

4 Jobs Available
##### Azure Administrator

An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems.

4 Jobs Available
##### Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack

3 Jobs Available
##### Automation Test Engineer

An Automation Test Engineer job involves executing automated test scripts. He or she identifies the project’s problems and troubleshoots them. The role involves documenting the defect using management tools. He or she works with the application team in order to resolve any issues arising during the testing process.

2 Jobs Available
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