Time and Work is an important topic of the arithmetic section for all Banking Railways and SSC exams. Here we are sharing some problems based on time and work, asked in various government exams.

Also, we are sharing various approaches that one can follow to solve Time and Work questions quickly. For better understanding, we split this article into two parts. In the first part, we will discuss the **basic approach of Time and work** with formulas, explanations, examples and see how the terms are related. In the second part, we will **explain the examples**.

More importantly, we will discuss** basics questions** asked in competitive exams and how we can solve them using the general process as well as the quick **Shortcut approach**.

**Part 1 (Time and work Concepts)**

**Time and work is** an important section of quantitative aptitude, where conceptual clarity of the relationship between working efficiency and time is very critical to understand.

#### Working Efficiency

Working efficiency is the work done by an individual in one day and this efficiency is inversely proportional to the number of the days to complete a job. It means that a person who takes fewer days to complete a job is said to be more efficient as compared to the other than a man who takes more days to complete the same job.

This relationship can be explained with the help of the following **example:**

If A can do a piece of work in 3 days and B can do the same work in 6 days, then in how many days they both will take to finish the work.

It is given that A body does a work in 10 days, hence the working efficiency of A is 1/3 work in one day. Similarly working efficiency of B 1/6work in one day. hence combined working efficiency of both of them in one day = (1/3+ 1/6) =1/2 work.

In other words, both of them working together will complete the work in 1/2 in one day.

Therefore, they will complete 1 work in **1/2 days**.

**From the above illustration, we conclude the following Results**

- Working efficiency is directly proportional to the number of persons assigned to complete the task or job.
- Working efficiency is inversely proportional to the number of days taken to complete a task or job.

Hence, if **A does** one work in **3 days and** **B does** the same work in **6 days**, then A is said to be twice as efficient as **B.**

These results can be used to find quick solutions for some *important questions*

## Time and Work Formulas

Below are some important formulae to solve some common problems of Time and work.

**How do you calculate time and work?**

We can solve or calculate Time and work problems using the following formulae, these are the most common and basic approaches to solve any tricky as well as simple problems for Time and work.

What is the easiest way to solve time and work questions?

What is the easiest way to solve time and work questions?

**Quick Tricks & Tips:**

If ‘**M**' is **'x'** times as good a workman as **'N', **then

a) The ratio of work done by** M**&**N **in equal time = **x: 1**

b) The ratio of time taken by **M**&**N**to complete the work = **1: x**. This means that **'M'** takes (1/x^{th}) time as that of '**N**' to finish the same amount of work.

**For example****,**

if M is twice efficient as good a workman as N, then it means that

a) M does twice efficient to perform work as done by N in equal time i.e. **M: N = 2:1**

b) M finishes his work in half the time as compared to N

**Chain Rule:**

the chain rule help to make the following relationship using the above formula we have :

**Relationship between Men and Work**.

More men ----------------> can perform-----------------> more work in more time

Less men ----------------> can perform ---------------> Less work in more time

**Relationship between Work and Time**

More work ----------------------->takes -----------------------> a lot of time to complete the task

Less work ---------------> takes -------------------->Less Time to complete the task

**Relationship between Men and Time**

More men ----------------->can do the task -----------------------> in more time

Less men -----------------> can do the task -----------------------> in more time

- X men can do a job in 1(t
_{1}) days and y man in 2 (t_{2})days, then (p men + q women) can do the work in.

5. x men or y women can do a work in t days, then (p men + q women) can do the same work in?

6. If a person X can do a work in ‘n’ days and X+BYtogether can do it in ‘T’ days, then Y alone can finish the work= {(T * n )/ (n-T ) }days.

**Time and work(Formulae)**

**Combined Work:**

a) **If 'M ' and 'N'**can finish the work in 'x' & 'y' days respectively, then

b) If 'M', 'N' & 'O' can complete the work in x, y & z days respectively, then

c) If **M can do a work in 'x' days** and if the same amount of work is done by **M & N together in 'y' days,** then

d) If **M & N** together perform some part of work in **'x' days**, **N & O **together perform it in **'y' days** and **O & M **together perform it in **'z' days**, then

If **M works alone, **then **deduct M's work** from the **total work of N & O **to find the **time taken by M alone.**

For M working alone, the time required will be =M's work - (M+N+O)'s combined work.

**e) Man -Work -Hour related problems:**

where,

**M: **Number of Men

**D: **Number of Days

**H: **Number of Hours

**W: **total Amount of Work done

If men are fixed, and the work is proportional to time. If work is fixed, then the time is inversely proportional to men. Thus we can conclude below results,

**Below are some important and simple concepts related to Time and Work.**

a) Work and time both are directly proportional to each other.

b) The number of men and time both are inversely proportional to each other.

c) And, work can be divided into equal parts It means if a task is completed in 5 days, one day you will finish (1/5^{th}) part of the work.

Try Free Online Quiz of Time and Work concepts in our free online test section here.

**Part 2 (T****ime and work Solved Problems)**

Below are some examples to try.

Have a keen look at the solution approach, this is one of the shortest approaches to the solution.

**Example 5: A can fabricate a divider in 40 days, while B alone can assemble it in 30 days If they construct it together and get an installment of RS. 7000, what B's offer?**

**Solution **

A's 1 days work = 1/40,

B's 1 day work = 1/30,

Proportion of their shares = 1/40:1/30 = 3:4

B's offer = (7000*4/7) = Rs. 4000

Author: Ashwani Kumar.

Ashwani Kumar is having more than 4 years of experience in preparing students on various government exams. Post your questions in the comment section and let our experts answer them.

**All the best.**

07-Apr-2020

## MOHD HARIS

Explainded in a very detailed way. Elaborating with example made it easy for me to understand quickly.07-Apr-2020

## Shariq Ali

All the concepts and their formulae are described very well with proper examples which made it easy to understand.08-Apr-2020

## Tushar Sharma

Nice