Practical Guide to Solving Time and Work Problems in CAT Quant

Time and Work is an important part of CAT Quant. It tests a student’s ability to link work, time, and efficiency. This article explains the key concepts, important formulas, and practical shortcuts to solve time and work questions quickly.

Table of Contents

Basic Concepts in CAT Time and Work
Time and Work Formula
Faqs

Practical Guide to Solving Time and Work Problems in CAT Quant

Time and Work in the CAT Exam is one of the important topics covered in the quant section. These topics measure the correlation between the amount of work done, the time taken to complete that amount of work done and the efficiency of an individual or group of individuals performing that work. Fundamentally, the concept is based on the important time and work formula where Work = Rate x Time. The rate is the efficiency of work or the amount of work a person can do in a given time.

Basic Concepts in CAT Time and Work

You can check the basic concepts behind time and work.

Time and Work Particulars	Details
Work	Work is defined as the task or job to be completed. In aptitude problems, the total work is usually assumed to be 1 unit or expressed in terms of efficiency or LCM-based units.
Work Rate / Efficiency	Work rate (or efficiency) is the amount of work done per unit time. If a person can complete a work in N days, then Efficiency = 1 / N (Work per Day) For example, If A can finish a job in 10 days, A’s 1-day work = 1/10 of the total work
Time	Time refers to the duration taken to complete a given work. It depends on work and efficiency, Time = Work / Efficiency
Combined Work	When two or more people work together, their combined efficiency is the sum of their individual efficiencies. If A does 1/10 work per day and B does 1/15 work per day, then together: A + B Efficiency = 1 / 10 + 1 / 15 = 1 / 6 Therefore, A and B together finish the work in 6 days
Work Equivalence	Work done is directly proportional to the time taken and efficiency. Work = Time x Efficiency
Inverse Relation between Time and Work	If the work is fixed, time and efficiency are inversely proportional Time ∝ 1 / Efficiency
Alternate Work (Work–Rest Pattern)	Sometimes workers work alternately (e.g., A one day, B the next day). In such cases, calculate the work done in 2-day cycles (A’s 1-day work + B’s 1-day work), then proceed accordingly.
Fraction of Work	If a person works for a certain number of days, the fraction of work completed is Fraction of work = Efficiency x Time worked

Time and Work Formula

Check the important formulas of time and work.

Particulars	Formulas
Work - Time Relation	Work = Rate of Work x Time Rate of Work = 1 / Time Taken
If A can do a work in x days and B can do the same work in y days, then	Work done by A in 1 day = 1 / x Work done by B in 1 day = 1 / y Work done by A and B together in 1 day = x + y xy Time taken by A and B together = xy x + y
Three Persons Work Formula	ABC AB + BC + CA
If A, B, C can do a work in x, y, z days respectively, then	Work done by A, B, C together in 1 day 1 + 1 + 1 x y z
Efficiency and Work	If A is k times as efficient as B, then Work done by A : Work done by B = k:1 Time taken by A : Time taken by B = 1:k

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FAQs

What are the common mistakes students make in Time and Work problems?

Forgetting to take the LCM of time values properly.
Mismanaging negative work (when a worker or pipe undoes work).
Not carefully reading conditions like “A is twice as efficient as B.”
Mixing up time taken with efficiency ratio.

How do I handle questions where workers leave or join midway?

Split the work into parts:

Calculate the work done till a point.
Deduct it from the total work.
Assign the remaining work to the new group of workers and calculate.

How do I calculate the efficiency of a person?

Efficiency is the amount of work done in one day (or one hour).

If a person completes a work in N days, then their efficiency = 1 / N of work per day.

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