Today we will discuss one of the important chapter from the quant section i.e., Time and Work.
Basic Concepts of Work and Time:
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.
Types of Questions and its Short Tricks
Case 1: A complete job will be considered = 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 = part of total work i.e. =
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 = part of total work.
Case 4: The reciprocal of 1 day’s work gives the individual time. i.e., time taken by a single persons to complete the job =
Example: Sunny can do 1/5th of an work in 1 day. In how many days can he complete the same work.
Solution: Time of completion by Sunny alone = individual time = = Therefore , sunny can complete the job alone in 5 days.
Case: 5: 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.
Example: A person ‘P’ can do a work in 15 days and ‘Q’ can do it in 20 days. What amount of work is done by P and Q together in one day?
Solution: (P+Q)’s 1 day work = P’s 1 day work + Q’s 1 day work. 1 day’s work =
We can find (P+Q)’s 1 day work = part of total work. So, 1 day work of P and Q =
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)
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 6: 1. The reciprocal of combined work done in 1 day gives the tome for completion by the persons working together.
i.e., time of completion == 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=
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 =
Now, as specified in case 5
Combined work in 1 day = sum of individual work done by Ram, Shaym and Kamal (Ram + Shyam+Kamal)’s 1 day work = Ram’s 1 day work + Shyam’s 1 day work +Kamal’s 1 day work = th part of work = 1/4th part of work
Time taken to complete the work = 4 days.
Case 7: Part of work done at any time ‘t’ by one or more persons = t × (1 day’s work)
Example: A persons ‘M’ can do a job in 25 days. How much of the job is done by him in 5 days?
Solution: Part of work done by M in 5 days = 5 × (1/25) = 1/5th part of work
Example: Two friends A and B can complete a piece of work in 12 days and 8 days respectively. Find the amount of work done by them in 4 days.
Solution: Part of work done by (A+B) in 4 days = 4 ×(A+B)’s 1 day work
= th part of work = 5/6th
Example: Two persons P and Q can do a piece of work individually in 10 days and 15 days respectively. If P work for 2 days and Q works for 5 days, then find the total amount of work done.
Solution: Part of work done by P + Q = Part of work done by P in 1 day + part of work done by Q in 5 days
= the part of work = 8/15th
Case 8: 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
Total work is finished in 11.25 days.
Case 9: The ration of the work done by the two persons in the same time is the inverse ratio of their individual time.
e.g., if ‘A’ can do a work in 5 days and B can do in 9 days, then, in the same time, ( inverse of time taken when working alone)
Case 10: If a person ‘P’ is ‘n’ times as good a workman as Q, individual time for
P = and after some time (using case 9)
Example: Tannu and Rekha can do a job in 12 days. Rekha alone can finish it in 36 days. In how many days can Tannu and alone finish the work?
Solution: (Tannu + Rekha)’s 1 days work = Tannu’s 1 day work + Rekha’s 1 day work
= Tannu’s 1 day work work + 1/36
Tannu’s 1 day work =th of work. So, Tannu can finish it in 18 days.
If T = 12, R = 36 then
Required time = = 18 days
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