**Dear Readers,**

**Numerical ability section** is considered to be one of the toughest subjects of** Competition Exams** but it can be scored off well if prepared well. **Time and Work **is one of the toughest chapters which leaves candidates a bit confused and most of the aspirants leave these questions untouched.

To make the chapter easy for you all, we are providing you with all some **Short Tricks to solve Time and Work Questions** which will surely make the chapter easy for you all.

** 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 is taken to complete an assigned job.

(B) **Individual time**:- Time needed by a 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’ complete a job alone in t days, then the time is taken by**’= 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 is taken by a single person to complete the job =

**Example**: Sunny can do 1/5^{th} of a 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 is 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 is 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 is 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’ 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 is working for different time schedules to complete a piece of work, then

(i) Assume the time for completion = T

(ii) The number of days worked by each person is found with reference to T, if not mentioned in the problem.

(iii) Some 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 at 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, at 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

**Thanks!**

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