Handy Tips For Solving Time And Work Aptitude Problems

Understanding time and work problems is not just crucial for acing maths exams but also for mastering practical problem-solving skills. Most competitive exams such as CAT, SSC CGL, SSC 10+2, and many more frequently feature quantitative aptitude sections where questions related to time, work, and rates are prominent. Concepts related to Time and Work are discussed across Class 8 to Class 10. In Class 8 chapter 13 ‘Direct and Proportions’ discusses concepts of inverse proportion, direct proportion, and many more that are used to solve work and time problems.

Understanding the tips and shortcuts outlined in this guide can significantly boost their problem-solving speed and accuracy, enabling them to tackle these types of questions effectively within the time constraints of the exam.

Understanding Basics

At its core, time and work problems revolve around the relationship between time, work done, and the rate at which work is completed. Whether it's calculating the time required for a team to build a structure or understanding the individual efficiency of workers, time and work problems demand a strategic approach and solid mathematical skills.

Rate of Work: How fast work is done, usually measured as work per unit time.

Efficiency: Measures the amount of work accomplished in a given time.

Basic Formula: Work = Rate × Time

Direct Proportion: More workers mean less time to finish a task.

Total Work = Number of Workers × Time Taken

Reciprocal Proportion: When work remains constant and the number of workers changes:

• If A can do a job in x days, A's daily work = 1/x

• If B can do the same job in y days, B's daily work = 1/y

• Combined work in a day = 1/x + 1/y

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Strategies To Solve The Problems

To excel in solving time and work problems, adopting certain strategies can significantly enhance problem-solving skills:

>> Breaking Down Complexities: One of the initial challenges with time and work problems is often the complexity of the scenarios presented. However, these problems can be simplified by breaking them down into smaller, manageable parts.

>> Visualisation and Conceptual Understanding: Visualising the problem aids in grasping the concept of work and time. Creating mental images of the task being performed and the time taken helps in understanding the problem better.

>> Practice and Familiarity: Proficiency in solving time and work problems develops through practice. Regular practice with different types of problems reinforces concepts and hones problem-solving skills, making solving these problems more intuitive.

>> Use of Real-Life Analogies: Relating mathematical problems to real-life situations enhances comprehension. Associating the scenarios presented in time and work problems with everyday tasks makes them relatable and easier to understand.

Practice Problems

Problem 1: A, B, and C take different amounts of time to finish a job. A finishes it in 20 days, B in 30 days, and C in 60 days. They all worked together for 5 days, then A left. After that, B and C worked together for 5 more days before B left. The rest of the work was finished by C. What part of the job did C finish?

Solution

A, B, C takes 20 days, 30 days, and 60 days respectively to finish the work.

A’s daily work = 1/20 part

B’s daily work = 1/30 part

C’s daily work = 1/60 part

They all worked for 5 days

Work done in 5 days = 5/20 + 5/30 + 5/60 = 1/4 + 1/6 + 1/12 = 1/2 part

B and C work for 5 more days

Work done in 5 more days = 5/30 + 5/60 = 1/6 +1/12 = 1/4

Remaining work

1 - 1/2 - 1/4 = 1/4

Total work done by C = 1/12 + 1/12 +1/4 = 1/6 + 1/4 = 5/12

Hence, total work done by C is 5/12 part

Shortcut Trick

Let suppose total work = 60 Unit

Rate of work of A = 60/20 = 3 unit/day

Rate of work of B = 60/30 = 2 unit/day

Rate of work of C = 60/60 = 1 unit/day

First 5 days all work together, then B and C work for 5 more days, remaining work completed by C.

Work done by C = 60 unit - 5*3 - 10*2 = 25 Unit

Part of work done by C = 25/60 = 5/12 part.

Problem 2: Person X finishes 20% of a job in 8 days, and person Y finishes 25% of the same job in 6 days. If they team up, how many days will it take for them to complete 40% of the job?

Solution:

X’s daily work = 20%/8 = (1/5)(1/8) = 1/40 part

Y’s daily work = 25%/6 = (1/4)(1/6) = 1/24 part

Both work together daily = 1/24 + 1/40 = (1/8){ 1/3 + 1/5}

= (1/8)(8/15) = 1/15 part

Time taken to complete 40% work

= 40%/(1/15) = (40/100)(15/1) = 6 days

Shortcut Trick

Let consider total work = 120 unit

X finish 20% work in 8 days

20% of 120 = 24

Rate of X = 24/8 = 3 unit /day

Y finish 25% in 6 days

25% of 120 = 30 unit

Rate of Y = 30/6 = 5 unit/day

Time taken to complete 40% of work

40% of 120 = 48 unit

Rate of X and Y together = 3 + 5 = 8 unit/day

Total time taken = 48/8 = 6 days.

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Hope this helps you understand things like rate of work, efficiency, proportion and how you can use these ideas to solve problems.