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# Time and Work Formulae

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## An Overview

Time and work are the topics that are interrelated to each other. The concept of time and work works on simple principles that are how much time a person takes to complete a certain task or how many people should be assigned a particular task to finish the same in a given time limit. Time and work deal with the number of people completing a piece of work, the efficiency of the work done by each of them, and the time taken by them. After understanding about work-time relationships, concepts like questions on speed, distance, and time become much easier.  For better understanding, let’s dive deeper and solve some questions on time and work.

Time & Work

## Time and Work Formulae

Time and Work Formula List

Time and work formulas are important to solve time work questions.

1. Work done = time taken × Rate of work

2. Rate of work done = $\dfrac{1}{\text{Time taken to finish a task}}$

3. Time taken to finish a task = $\dfrac{1}{\text{Rate of work done}}$

4. If the number of days in which a task is done is given as ‘n’, then work done in one day will be $\dfrac{1}{n}$

5. Total work done = numbers of days taken to complete a task × Efficiency

## The Basic Types of Questions Related to Time and Work

• Questions on time taken by an individual or group of individuals to complete a piece of work.

• Questions to find the number of people required to complete a given task

• Questions to find the efficiency of an individual

• Questions to find the speed of an individual or a group of individuals to complete a task

## Solved Examples

1. Palak and Kajal can complete a project in 30 days. Palak worked for 16 days and kajal completed the remaining work in 44 days. How many days would Kajal have taken to complete the entire project by herself?

Ans: Let the work done by Palak in 1 day be x

Let the work done by Kajal in 1 day be y

Then, x+y=$\dfrac{1}{30}$—------------(1)

16x+44y=1—----------------(2)

By solving, we get,

x=$\dfrac{1}{60}$

y=$\dfrac{1}{60}$

Kajal can complete the work in 60 days.

2. Monika and Radhika can do a task in 4 days, while Tanu and Ana can do the same task in 12 days. In how many days will they do it together?

Ans: Monika, Radhika, Tanu, and Ana will together take $\dfrac{1}{4} + \dfrac{1}{12} = \dfrac{4}{12}$ i.e. $\dfrac{1}{3}$

They will take 3 days to complete the task.

3. Ram can do work in 8 days, which Amir can alone do in 10 days. In how many days both cooperating can do it?

Ans: Ram’s one-day work = $\dfrac{1}{8}$

Amir’s one-day work = $\dfrac{1}{10}$

(Ram + Amir)’s one day work = $\dfrac{1}{8}$ + $\dfrac{1}{10}$ = $\dfrac{9}{40}$

Both can do the work in $\dfrac{40}{9}$ days.

4. Aman takes x hours to mow a lawn. In one hour, what part of the lawn is mowed?

Ans: Total time is taken by Aman to mow a lawn= x hours

Lawn mowed in one hour= $\dfrac{1}{x}$

5. John finishes work in 18 days and Reeta finishes the same work in half the time taken by John. Working together, what part of the same work can they finish in a day?

Ans: Time is taken by John = 18 days

Time taken by Reeta = $\dfrac{18}{2}$=9 days

(John + Reeta)’s 1 day work = $\dfrac{1}{18}$+$\dfrac{1}{9}$=$\dfrac{1}{6}$

## Practice Problems

1. Person A can paint a house in 10 days. Person B requires 15 days for the same work. If person A and person B work together, how many days will the work require?

(a) 6 days

(b) 8 days

(c) 5 days

(d) 9 days

Ans: 6 days

2. Tony and Sam can paint a wall in 72 hours, and Sam and Bruce can do the same work in 120 hours. But Tony and Bruce can do it in 90 days. At what time can Tony, Sam, and Bruce do the work when all three work together?

(a) 80 hours

(b) 66 hours

(c) 60 hours

(d) 75 hours

Ans:60 hours

3. Salman can make one toy car in 5 days, but with the help of his son, he can do it in 3 days. In how much time can the son do it alone?

(a) $6\dfrac{1}{2}$ days

(b) 7 days

(c) $7\dfrac{1}{2}$ days

(d) 8 days

Ans: (c) $7\dfrac{1}{2}$ days

4. Lata and Ram are working on an assignment. Lata takes 6 hours to type 32 pages on a computer while Ram takes 5 hours to type 40 pages. How much time will they take, working together on two different computers, to type an assignment of 110 pages?

(a) 7 hrs 30 min

(b) 8 hrs and 15 min

(c) 8 hrs

(d) 8 hrs 25 min

Ans: 8 hrs and 15 min

5. Sam can do $\dfrac{1}{3}$ of the work in 5 days and Karl can do $\dfrac{2}{5}$ of the work in 10 days. In how many days can both Sam and Karl together do the work?

(a) $7\dfrac{3}{4}$ days

(b) 10 days

(c) $9\dfrac{3}{8}$ days

(d) $8\dfrac{4}{5}$ days

Ans: $9\dfrac{3}{8}$ days

Worksheet

## Summary

The concept of time and work can be applied in real life as well. There are many situations where we have to apply basic time and work formulas to find out certain things. Since time and work questions have real-life implications, learning and solving questions on time management and questions on time complexity become more important. One has to learn the above formulas at the fingertips as they make solving the questions easier. Solving and practising problems can also help in mastering the concept of time and work.

Last updated date: 26th Sep 2023
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## FAQs on Time and Work Formulae

1. What is the relation between time and work?

Time and work are directly proportional to each other.

2. Which units are inversely proportional in time and work concept?

The ratio of time taken by two workers and their efficiencies are inversely proportional to each other.

3. What is the formula for finding out the number of days when work is given?

Number of days = Total work/ Work done in one day.