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NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities: In our daily life, we compare many things like his bottle is filled up to twothirds of its height, his mark is 66% of my mark, my marks increased by 15% compared to the last test, etc. In this chapter of NCERT, you will learn to compare quantities using ratios, percentage. Also, you will learn concepts of profit, loss and simple interest. In CBSE NCERT solutions for Class 7 Maths chapter 8 Comparing Quantities, you will get questions related to the above concepts which are useful in our daily life for the basics for calculations in our life. Ratio and percentage are two things which are useful in comparing quantities. It is advisable that students must complete the NCER Class 7 Maths Syllabus to the earliest in revise in a better way.
There are 24 questions in three exercises of in Class 7 NCERT Maths chapter comparing quantities . You will get solutions to all these questions in CBSE NCERT solutions for Class 7 Maths chapter 8 Comparing Quantities explained in a detailed manner. You will get NCERT Solutions from Classes 6 to 12 by clicking on the above link. Here you will get NCERT Solutions for Class 7.
Percent Calculation: Percent = (Part / Whole) × 100
Part (How Many) = (Percent / 100) × Whole
Conversion: Fraction or Decimal to Percent = (Fraction or Decimal) × 100
Percent to Fraction or Decimal = Percent / 100
Increase or Decrease as Percent: Percentage Increase = (Amount of Change / Original Amount) × 100
Percentage Decrease = (Amount of Change / Original Amount) × 100
Cost Price (CP) and Selling Price (SP): CP = Buying price of any item.
SP = Price at which item sells.
If CP < SP → Profit = SP  CP
If CP > SP → Loss = CP  SP
If CP = SP → No profit, No loss
Profit percent = (Profit / CP) × 100
Loss Percent = (Loss / CP) × 100
Simple Interest (S.I.): S.I. = (Principal × Rate × Time) / 100
Amount = Principal + Interest
Percent Calculation: Percent represents a part of a whole, expressed as a fraction of 100.
Conversion: You can convert fractions or decimals to percentages by multiplying them by 100. Similarly, to convert percentages to fractions or decimals, you divide the percentage by 100.
Increase or Decrease as Percent: You can find the percentage increase or decrease by comparing the change in value to the original value.
Cost Price (CP) and Selling Price (SP): Cost Price (CP) is the price you pay for an item, and Selling Price (SP) is the price at which you sell it. If SP is higher than CP, you make a profit. If SP is lower, you incur a loss.
Simple Interest (S.I.): Simple Interest is a way to calculate the extra amount you earn or pay on a sum of money over time. It depends on the principal amount, the interest rate, and the time period.
Question:1 Find the ratio of:
(a) Rs 5 to 50 paise
(b) 15 kg to 210 g
(c) 9 m to 27 cm
(d) 30 days to 36 hours
Answer: (a) Rs 5 to 50 paise
First, convert the given quantities into the same units,
So, Rs 5 = = 500 paise
Now, Ratio =
(b) 15 kg to 210 g
Converting the given quantities into the same unit.
So, 15 kg = = 15,000 g
Therefore, Required ratio
(c) 9 m to 27 cm
First, convert meter into centimetre
So, 9m =
Therefore, the required ratio
(d) 30 days to 36 hours
Converting the given quantities into the same unit.
So, 30 days =
Therefore, the ratio
Answer: Given that,
6 student use 3 computers
So, 1 computer is used by students.
Therefore, for 24 students no. of computer required = computers
Hence the required number of computer is 12.
(i) How many people are there per in both these States?
(ii) Which State is less populated?
Answer: Given that,
Population of Rajasthan = 570 lakhs and population of UP = 1660 lakhs
Area of Rajasthan =
and area of UP =
Now,
(a) Number of peoples per
In Rajsthan, =
In UP,
= 580
(b) Rajasthan is less populated as we can see that the number of people in per is less
Height  Number of Children  In Fraction  In Percentage 
110 cm  22  
120 cm  25  
128 cm  32  
130 cm  21  
Total  100 
Answer:
Height  No. of children  In fraction  In percentage 
110  22  22/100 =0.22  22% 
120  25  25/100 = 0.25  25% 
128  32  32/100 =0.32  32% 
130  21  21/100 =0.21  21% 
total  100  01  100% 
Question:2 A shop has the following number of shoe pairs of different sizes.
Size 2 : 20 Size 3 : 30 Size 4 : 28 Size 5 : 14 Size 6 : 8
Write this information in tabular form as done earlier and find the Percentage of each shoe size available in the shop.
Answer:
Size  No. of shoes  Fraction  Percentage 
2  20 


3  30 


4  28 


5  14 


6  8 


Total  100 
Question:1 A collection of 10 chips with different colours is given.
Colour  Number  Fraction  Denominator Hundred  In Percentage 
Green  
Blue  
Red  
Total 
Fill the table and find the percentage of chips of each colour.
Answer:
Colour  Number  Fraction  Denominator hundred  In percentage 
Green  4  4/10=0.4  40/100  40% 
Blue  3  3/10=0.3  30/100  30% 
Red  3  3/10=0.3  30/100  30% 
Total  10  1  100/100  100% 
Answer: We have,
Number of gold bangles = 20
Number of silver bangles = 10
Total bangles = 30
Therefore, the percentage of gold bangles
and the percentage of the silver bangles
Question:1(a) Convert the following to per cents:
Answer:
To convert into a percentage,
Question:(e) Convert the following to per cents:
0.05
Answer: (e) 0.05
To convert into a percentage,
Question:2(i) Out of 32 students, 8 are absent. What per cent of the students are absent?
Answer: We have a total number of student = 32
and the absent student = 8
Therefore, the percentage of absent students
Question:2(ii) There are 25 radios, 16 of them are out of order. What per cent of radios are out of order?
Answer: We have a total radio = 25
and the radios that are out of order = 16
Therefore, the percentage of out of order radios
Question:2(iii) A shop has 500 items, out of which 5 are defective. What per cent are defective?
Answer: Given that,
The shop has total items =500
Defective item = 5
Therefore, the percentage of the defective item
Question:2(iv) There are 120 voters, 90 of them voted yes. What per cent voted yes?
Answer: Given that,
The total no. of voters =120
Voted yes = 90
Therefore, the percentage of voted yes
Question:1(i) 35% + _______ = 100%
Answer: Let the blank space be X
therefore, 35% + X = 100%
So, X = 100%  35%
= 65%
Question:1(ii) 64% + 20% +________ % = 100%
Answer: Let the blank space be X
therefore,
64% + 20% + X = 100%
So, X = 100%  64%  20%
= 16%
Question:1(iii) 45% = 100% – _________ %
Answer: Let the blank space be X
therefore,
45% = 100%  X
So, X = 100%  45%
= 55%
Question:1(iv) 70% = ______% – 30%
Answer: Let the blank space be X
therefore,
70% = X  30 %
So, X = 70% 30%
= 100%
Question:2 If 65% of students in a class have a bicycle, what per cent of the student do not have bicycles?
Answer: Given that,
65 % of students in a class have a bicycle.
So, the remaining percent of students have no bicycle
= 100%  65%
= 35%
Hence 35% of students have no bicycle.
Answer: We have,
A basket is full of apples, oranges and mangoes.
50% are apples, 30% are oranges.
So, the remaining percent are mangoes = 100%  50%  30%
= 20%
Question:1(a) What per cent of this figure is shaded?
You can make some more figures yourself and ask your friends to estimate the shaded parts.
Answer: In the above figure, there are a total of 4 parts and out of which 3 parts are shaded
therefore, the percentage of the shaded part
Question:1(b) What per cent of this figure is shaded?
You can make some more figures yourself and ask your friends to estimate the shaded parts.
Answer: In the above figure,
The total shaded part =
Therefore, the percentage of the shaded part
Question:1(a) Find: 50% of 164
Answer:
50% of 164
So 50% of 164 is 82, that is half of 164
Question:1(b) Find: 75% of 12
Answer: 75% of 12
Answer: We have,
8% children of a class of 25 like getting wet in the rain
therefore, the number of children get wet
8 % of 25
Hence out of 25 only 2 children get wet in the rain
Question:1 9 is 25% of what number?
Answer: Let the number be X
therefore, 25% of X = 9
Question:2 75% of what number is 15?
Answer: Let the number be X
therefore, 75% of X = 15
Question:1 Convert the given fractional numbers to per cents.
Answer: To convert the given fractional into the per cent we have to do multiplication in numerator and denominator by 100
Now,
Question:2 Convert the given decimal fractions to per cents.
(a) 0.65
(b) 2.1
(c) 0.02
(d) 12.35
Answer: To convert the given fractional decimal into a per cent, multiply the denominator and numerator by 100.
So,
(a) 0.65
(b) 2.1
(c) 0.02
(d) 12.35
Question:3(i) Estimate what part of the figure is coloured and hence find the per cent which is coloured.
Answer: We have,
The fraction of the coloured part =
Therefore,
Question:3(ii) Estimate what part of the figure is coloured and hence find the per cent which is coloured.
Answer: In the given figure, the fraction of the coloured part is
Therefore, Percentage of the coloured part
Question:3(iii) Estimate what part of the figures is coloured and hence find the per cent which is coloured.
Answer: In the given figure, the fraction of the coloured part is
Therefore, Percentage of the coloured part
Question:4 Find: (a) 15 of 250
(b) 1 of 1 hour
(c) 20 of Rs 2500
(d) 75 of 1 kg
Answer: Here per cent implies for ( )
Therefore,
(a) 15% of 250
= 37.5
(b) 1 of 1 hour
= 1 of 60 minutes
(c) 20 of Rs 2500
(d) 75 of 1 kg
We know that 1kg = 1000 gm, therefore,
=0.75 kg
Question:5 Find the whole quantity if
(a) 5% of it is 600.
(b) 12% of it is Rs 1080.
(c) 40% of it is 500 km.
(d) 70% of it is 14 minutes.
(e) 8% of it is 40 litres.
Answer: (a) Let the whole quantity be X
Therefore, 5 % of X = 600
Thus the required whole quantity is 12000
(b) 12 % of X = Rs 1080
(c) 40 % of X = 500 km
(d) 70% of X = 14 minutes
(e) 8 % of X = 40 litre
Question:6 Convert given per cent to decimal fraction and also to fraction in simplest forms:
(a) 25%
(b) 150%
(c) 20%
(d) 5%
Answer: (a) 25 %
(b) 150%
(c) 20%
(d) 5%
Question:7 In a city, 30% are females, 40% are males and remaining are children. What per cent are children?
Answer: Given that,
30 % are female and
40 % are males
Total percentage of females and males
= 30 % + 40% = 70%
Therefore, Percentage of children
= (100% 70%) = 30 %
Answer: Given that,
Total number of voters = 15000
Percentage of voters who voted = 60%
Therefore, remaining 40% voters didn't vote
Thus, the number of people who did not vote
=
Question:9 Meeta saves Rs 4000 from her salary. If this is 10% of her salary. What is her salary?
Answer: Given that,
10 % of her salary = 4000
Let her total salary be X
Therefore,
10% of X = 4000
X = Rs 40,000
Question:10 A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?
Answer: Given that,
Total match played by the cricket team = 20
and, a match won = 25%
According to question,
Number of winning match = 25 % of 20
hence they won total 5 matches out of 20 match
Question:1 Divide 15 sweets between Manu and Sonu so that they get 20 % and 80 % of them respectively.
Answer: We have 15 sweets.
Manu wants 20% and Sonu wants 80% of the sweets respectively.
Therefore, 20% of 15
=
and 80% of 15 sweets
Hence give 3 sweets to Manu and 12 sweets to Sonu.
Question:2 If the angles of a triangle are in the ratio 2 : 3 : 4. Find the value of each angle.
Answer: We have,
angles of a triangle are in the ratio 2 : 3: 4.
Let the angle be respectively
And the sum of all the angle
[by angle sum property]
so,
now, the angles are
40, 60 and 80
Question:1 Find Percentage of increase or decrease:
– Price of the shirt decreased from Rs 280 to Rs 210.
– Marks in a test increased from 20 to 30.
Answer: (i) The decrease in price is 280210=70
Percentage of decrease
= 25%
(ii) increase of mark is 3020=10
Percentage of increase
= 33.33%
Answer: Total increase in petrol = 52 1 = Rs51
Therefore, the percentage of price increase
Question:1 A shopkeeper bought a chair for Rs 375 and sold it for Rs 400. Find the gain Percentage.
Answer: We have,
SP = 400
CP =375
So, SP  CP = 25
SInce SP > CP
Therefore, Gain(%)
Question:2 Cost of an item is Rs 50. It was sold with a profit of 12%. Find the selling price.
Answer: We have,
CP = Rs 50
Profit = 12 %
SP = ?
Therefore,
Put the values in the above equation, we get
Question:3 An article was sold for Rs 250 with a profit of 5%. What was its cost price?
Answer: We have,
SP = Rs 250
Profit = 5%
CP =?
Therefore,
put the values in the above equation, we get
Question:4 An item was sold for Rs 540 at a loss of 5%. What was its cost price?
Answer: We have,
SP = Rs 540
Loss = 5%
CP =?
Therefore,
put the values in the above equation, we get
Question:1 Rs 10,000 is invested at 5% interest rate p.a. Find the interest at the end of one year.
Answer: Given that,
Principal = 10,000
Rate= 5% p.a
T = 1 year
Therefore,
Substituting the values in the above formula, we get
Answer: Given that,
Principal = 3,500
Rate= 7% p.a
T = 2 year
Therefore,
Substituting the values in the above formula, we get
Answer: Given that,
Principal = 6050
Rate= 6.5% p.a
T = 3 year
Therefore,
Substituting the values in the above formula, we get
So, the total amount to be paid = Rs 1179.75 + Rs 6050 =Rs 7229.75
Answer: Given that,
Principal = 7,000
Rate= 3.5% p.a
T = 2 year
Therefore,
Substituting the values in the above formula, we get
So, the total amount to be paid = Rs 490 + Rs 7000 =Rs 7490
Answer: Given that,
Principal = 2,400
Rate= 5% p.a
T = ?
Interest = Rs 240
Therefore,
Substituting the values in the above formula, we get
Answer: Given,
Simple Interest, S.I.=
Time,
Rate,
We know,
Therefore, the sum is
Question:1(a) Tell what is the profit or loss in the following transaction. Also find profit per cent or loss per cent in each case.
Gardening shears bought for Rs 250 and sold for Rs 325.
Answer: Given that,
Selling price = Rs 325
Cost price = Rs 250
Since SP > CP
Therefore, profit = SPCP = Rs 75
And, Profit %
Question:1(b) Tell what is the profit or loss in the following transaction. Also find profit per cent or loss per cent in each case.
A refrigerator bought for Rs 12,000 and sold at Rs 13,500.
Answer: Given that,
CP = Rs 12000
SP = Rs 13500
SInce SP > CP
Therefore, Profit = SP  CP = 1500
and, Profit %
Question:1(c) Tell what is the profit or loss in the following transactions. Also find profit per cent or loss per cent in each case.
A cupboard bought for Rs 2,500 and sold at Rs 3,000.
Answer: We have,
CP = Rs 2500
SP = Rs 3000
Since SP > CP
Therefore, Profit = SP  CP = 500
and, Profit %
Question:1(d) Tell what is the profit or loss in the following transaction. Also find profit per cent or loss per cent in each case.
A skirt bought for Rs 250 and sold at Rs 150.
Answer: We have,
SP = Rs 150
CP = Rs 250
Since CP > SP
Therefore, Loss = CPSP = Rs 100
and, Loss%
Question:2(a) Convert each part of the ratio to percentage:
3 : 1
Answer: (a) 3: 1
The total sum of the ratio is 3 + 1 = 4
Therefore, the percentage of the first part
Percentage of the second part
Question:2(b) Convert each part of the ratio to percentage:
2 : 3: 5
Answer: (b) 2 : 3: 5
Sum of the ratio part = 2 + 3 + 5 = 10
Therefore, the percentage of the first part
the percentage of the second part
the percentage of the third part
Question:2(c) Convert each part of the ratio to percentage:
1:4
Answer: (c) 1:4
Sum of the ratio part = 4 + 1 = 5
therefore, the percentage of the first part
the percentage of the second part
Question:2(d) Convert each part of the ratio to percentage:
1 : 2 : 5
Answer: (d) 1 : 2 : 5
Sum of the ratio part = 1 + 2 + 5 = 8
therefore, the percentage of the first part
the percentage of the second part
the percentage of the third part
Question:3 The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.
Answer: Given that,
Initial population = 25,000
Final population = 24,500
Total decrement = 1000 (25000  24500)
Therefore, percentage in decrease
Answer: Given that,
Original price (OP) = 3,50,000
Increased price (IP) = 3,70,000
Therefore, increase in price = OP  IP = 20,000
Thus, percentage of the increase price
Question:5 I buy a T.V. for Rs 10,000 and sell it at a profit of 20%. How much money do I get for it?
Answer: Here we have,
CP = Rs 10,000
Profit =
SP =?
We know that,
...........(i)
By substituting the values in eq (i), we get
= Rs 12,000
Answer: We have,
Sp of the washing m/c = Rs 13,500
Loss(%) = 20%
CP = ?
We know that,
Putting the values in the above equation we get;
Therefore,
Question:7(i) Chalk contains calcium, carbon and oxygen in the ratio 10:3:12. Find the percentage of carbon in chalk.
Answer: We have,
The ratio of calcium, carbon and oxygen in the chalk = 10 : 3: 12
Now, Sum of the ratio = 10 + 3 + 12 = 25
Therefore, the percentage of carbon in the chalk
Question:7(ii) If in a stick of chalk, carbon is 3g, what is the weight of the chalk stick?
Answer: We have the weight of the carbon = 3g
Therefore, the weight of the chalk
Hence the weight of the chalk is 25g
Question:8 Amina buys a book for Rs 275 and sells it at a loss of 15%. How much does she sell it for?
Answer: Here we have,
CP of the book = Rs 275
Loss = 15%
We know that,
Hence the required selling price is Rs 233.75
Question:9(a) Find the amount to be paid at the end of 3 years in this case:
Principal = Rs 1,200 at 12% p.a.
Answer: Given that,
Principal (PA)= Rs 1,200 at 12% p.a. (Rate of interest)
and T = 3 year
We know that,
Now, putting the values in the above equation, we get
So, Amount = PA + PI = 1200 + 432 = Rs 1632
Question:9(b) Find the amount to be paid at the end of 3 years in this case:
(b) Principal = Rs 7,500 at 5% p.a.
Answer: Given that,
Principal (PA)= Rs 7,500 at 5% p.a. (Rate of interest)
and T = 3 year
We know that,
Now, putting the values in the above equation, we get
So, Amount = PA + PI = 7,500 + 1125 = Rs 8625
Question:10 What rate gives Rs 280 as interest on a sum of Rs 56,000 in 2 years?
Answer: Given that,
Principal = Rs 56,000
Interest = Rs 280
Time = 2 year
Rate= ?
Therefore,
Question:11 If Meena gives an interest of Rs 45 for one year at 9% rate p.a. What is the sum she has borrowed?
Answer: Given that,
Principal =?
Interest = Rs 45
Time = 1 year
Rate= 9% p.a
Therefore,
Hence she borrowed a total Rs 500
8.1 Introduction
8.2 Equivalent Ratios
8.3 Percentage – Another Way Of Comparing Quantities
8.3.1 Meaning Of Percentage
8.3.2 Converting Fractional Numbers To Percentage
8.3.3 Converting Decimals To Percentage
8.3.4 Converting Percentages To Fractions Or Decimals
8.3.5 Fun With Estimation
8.4 Use Of Percentages
8.4.1 Interpreting Percentages
8.4.2 Converting Percentages To “How Many”
8.4.3 Ratios To Percents
8.4.4 Increase Or Decrease As a percent
8.5 Prices Related To An Item Or Buying And Selling
8.5.1 Profit Or Loss As A Percentage
8.6 Charge Given On Borrowed Money Or Simple Interest
8.6.1 Interest For Multiple Years
Ratio: The ratio tells how many times one number contains another. The unit must be the same to find the ratio of two quantities. If it is not same, you first convert it into the same unit then find the ratio.
Example Find the ratio of 500 meters and 1 Km.
First, we have to convert it to the same unit. 1Km=1000m. Now the ratio is 500:1000 or 1:2. In solutions of NCERT for Class 7 Maths chapter 8 Comparing Quantities, there are many problems where you will be using the above concept to find the ratio of quantities.
Percentage: It simply means numbers or amount in each hundred. In other words, percentages are number or ration that represents a fraction of 100. It is represented by '%'. 5% means 5 out of 100. That is 5/100= 0.05. Let's see an example to calculate the percentage
Example: Out of 50 students there are 20 boys in the class then what is the percentage of girls in the class?
Solution:
60% of students are girls. That is 5020=30 are girls.
Chapter No.  Chapter Name 
Chapter 1  
Chapter 2  
Chapter 3  
Chapter 4  
Chapter 5  
Chapter 6  
Chapter 7  
Chapter 8  Comparing quantities 
Chapter 9  
Chapter 10  
Chapter 11  
Chapter 12  
Chapter 13  
Chapter 14  
Chapter 15  Visualising Solid Shapes 
There are two additional topics profit and loss percentage and simple interest in this chapter. The last exercise of NCERT solutions for Class 7 Maths chapter 8 Comparing Quantities has all 11 questions related to these two topics.
Profit and Loss Percentage: If the selling price (SP) > cost price (CP) then there is a profit P= SPCP. If selling price (SP) is < cost price (CP) then there is a loss L= CPSP.
Simple interest: If we deposit 100 rupees for the interest of 10% for a year then you will get 100+10% of 100=100+10=110 rupees after a year. Here 100 rupees is known as the principal or sum (P), 10% is the rate per cent per annum (R), Then the interest we are getting (I) after 1 year is (If we are borrowing money then the interest is to be paid)
The amount (A) you will receive total amount = Principle amount +Interest =100+10=110
Suppose if you are borrowing or taking a loan for more than one year (say T years) then the interest to be paid after T years is
There are practice questions given after every topic to get a better understanding of the concept. In CBSE NCERT solutions for class 7 maths chapter 8 comparing quantities, you will also get solutions to practice questions given after every topic. Solve all the questions and examples to understand the concept and score well in the exam.
Happy learning!!!
Also Check NCERT Books and NCERT Syllabus here:
The concepts of NCERT Maths chapter comparing quantities are helpful in higher classes as well as in real life. The calculations based on percentage, ratios, simple interest, profit and loss etc are used in real life in many situations.
There are 3 exercises in NCERT solution Class 7 chapter 8. Students can practice these maths class 7 chapter 8 solutions to command the concepts that ultimately lead to score well in the exam.
Here are the topics covered in NCERT Class 7 Maths Chapter 8
8.1 Introduction
8.2 Equivalent Ratios
8.3 Percentage – Another Way Of Comparing Quantities
8.3.1 Meaning Of Percentage
8.3.2 Converting Fractional Numbers To Percentage
8.3.3 Converting Decimals To Percentage
8.3.4 Converting Percentages To Fractions Or Decimals
8.3.5 Fun With Estimation
8.4 Use Of Percentages
8.4.1 Interpreting Percentages
8.4.2 Converting Percentages To “How Many”
8.4.3 Ratios To Percents
8.4.4 Increase Or Decrease As a percent
8.5 Prices Related To An Item Or Buying And Selling
8.5.1 Profit Or Loss As A Percentage
8.6 Charge Given On Borrowed Money Or Simple Interest
8.6.1 Interest For Multiple Years
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