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 1/5^{th} 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=

**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 = 1/4^{th} 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) = 1/5^{th} 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 = 5/6^{th}

**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 = 8/15^{th}

**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.

**Trick :**

If T = 12, R = 36 then

Required time = = 18 days

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