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)

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 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=