Though it is one of the smaller topics of CAT, Time & Work questions are relatively easy and every candidate should not miss out on any of the questions from the topic. Here we have a comprehensive view on the Strategy of Work and Time along with a few practice questions
In solving the problems based on time and work, we need to calculate the following parameters.
(A) Time : – Time taken to complete an assigned job.
(B) Individual time :- Time needed by single person to complete a job.
(C) Work:- It is the amount of work done actually.
QUESTIONS HANDLING STRATEGY
- Work from Days : If A can do a piece of work in n days, then A’s 1 day’s work =1/n
- Days from Work : If A’s 1 day’s work =1/n, then A can finish the work in n days.
If A is thrice as good a workman as B,then :
Ratio of work done by A and B = 3:1.
Ratio of time taken by A and B to finish a work = 1:3.
For similar tips and concepts on SET THEORY, you can download Set-theory
Once we are done with the basics, we have to have a look on all the types of questions available. Lets have each one of them on by one.
Case 1: A complete job isconsidered = 1
Case 2: Assume a person ‘M’ complete a job alone in t days, then time taken by ‘M’= t
Case 3: 1 day’s work by any person = 1/t
Example:– Ram can whitewash a building in 17 days. Find the work done by Ram in one day.
Solution: Here, time taken by Ram = 17 days, so 1 day’s work by Ram = 1/17th part of total work.
Case: 4: When more than one person are working on the same piece of work then their combined 1 day’s work = sum of 1 day’s work by each person. i.e., if A, B and C are three persons working on a job, then (A+B+C)’s 1 day’s work = A’s 1 day work + B’s 1 days work + C’s 1 days work.
Corollary: Work done by A in 1 day = 1 day work of (A+B+C) – (1 day work of B + 1 day work of C) Similarly, Work done by B in 1 day = work done by (A+B+C) in 1 day – (work done by A in 1 day + work done by C in 1 day)
Case 5: 1. The reciprocal of combined work done in 1 day gives the time for completion by the persons working together.
i.e., time of completion = 1/combined = 1 day’s work.
2. It implies that if three persons, say , A, B and C are working together on a job, then Time for completion of work by them= 1/( A+B+C)’s one day work
Example: Three persons Ram, Shyam and Kamal can do a job in 10 days, 12 days and 15 days respectively. In how many days can they finish the job working together?
Solution: Time for completion of work = 1/ combined work (A+B+C)
Case 6: If more than one person are working for different time schedules to complete a piece of work, then
(i) Assume the time for completion = T
(ii) Number of days worked by each persons in found with reference to T, if not mentioned in the problem.
(iii) Sum of the parts of work done by each person = 1, since the job is complete.
Example: Deepak and Anil can do a piece of work in 10 days and 30 days respectively. They work together and Deepak leaves 5 day’s before the work is finished. Anil finishes the remaining work alone. In how many days is the total work finished?
Solution: Assume the time for completion = T
Since Deepak leaves 5 days before the work is finished.
So, no. of days worked by Deepak = T – 5 and Anil works, so, number of days worked by Anil = T
Deepak’s work + Anil’s work – 1
So we have = T-5/10 + T/30 =1
T = 11.25
A serious candidate should take all these steps seriously and solve all the questions have he come across, This will definitely get him/her the desired score.
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