## A Brief Explanation of Work Done Problems

Work problems typically occur when two people are painting a house together. You are typically asked how long it takes each individual to paint a house of a comparable size and how long it will take the two of them to paint the house when they collaborate. So, here the concept of work done will be used. In this article, we will learn how we can solve the work done problems.

## Work Done Related Important Formula

In time and work, we will learn to calculate and determine the number of hours needed to complete a task as well as the amount of work completed in a specific period of time. We are aware that a person's productivity is closely correlated with the time it takes him to do a task.

For Example: Suppose Shyam can finish a work in 7 days.

Then, work done by Shyam in 1 day $=\dfrac{1}{7}$

Rules:

Suppose if a person A can finish a work in $\mathrm{n}$ days.

Then, work done by $A$ in 1 day $=1 / n^{\text {th }}$ part of the work.

Suppose that the work done by $\mathrm{A}$ in 1 day is $\dfrac{1}{n}$

Then, time taken by $\mathrm{A}$ to finish the whole work $=\mathrm{n}$ days.

## Solved Problems on Work Done

Here are some solved problems on work done, through which it can be understood in a better way:

Q1. Piyush and Rahul together can complete a work in 18 days. Piyush alone can do the same work in 24 days. What will be the number of days Rahul alone can complete the whole work?

Ans: Piyush and Rahul can complete the work in 18 days

Piyush alone can complete the work in 24 days

Taking the L.C.M of 18 and 24

L.C.M of 18 and 24 is 72

$\Rightarrow$ One day work of Piyush and Rahul $=\dfrac{72}{18}=4$

$\Rightarrow$ One day work of Piyush $=\dfrac{72}{24}=3$

$\Rightarrow$ One day work of Rahul $=4-3=1$

$\Rightarrow$ Number of days Rahul alone takes to complete the work $=\dfrac{72}{1}=72$

$\therefore$ The number of days Rahul takes to complete the whole work is 72.

Q2. A and $B$ together can do a piece of work in 15 days, while $B$ alone can finish it in 20 days. In how many days can $A$ alone finish the work?

Ans: Time taken by $(A+B)$ to finish the work $=15$ days.

Time taken by B alone to finish the work is 20 days.

$(A+B)$ 's 1 day's work $=\dfrac{1}{15}$

and $B^{\prime}$ s 1 day's work $=\dfrac{1}{20}$

A's 1 day's work $=\left\{(A+B)^{\prime}\right.$ s 1 day's work $\}-\left\{B^{\prime}\right.$ s 1 day's work $\}$

$=(\dfrac{1}{15}-\dfrac{1}{20})=\dfrac{4-3}{60}=\dfrac{1}{60}$

Therefore, A alone can finish the work in 60 days.

Q 3. A can do a piece of work in 25 days and $B$ can finish it in 20 days. They work together for 5 days and then A leaves. In how many days will $B$ finish the remaining work?

Ans: Time taken by $\mathrm{A}$ to finish the work $=25$ days.

A's 1 day's work $=\dfrac{1}{25}$

Time taken by $B$ to finish the work $=20$ days.

B's 1 day's work $=\dfrac{1}{20}$

$(A+B)$ 's 1 day's work $=(\dfrac{1}{25}+\dfrac{1}{20})=\dfrac{9}{100}$

$(A+B)$ 's 5 day's work $(5 \times \dfrac{9}{100})=\dfrac{45}{100}=\dfrac{9}{20}$

Remaining work $(1-\dfrac{9}{20})=\dfrac{11}{20}$

Now, $\dfrac{11}{20}$ work is done by $B$ in 1 day

Therefore, $\dfrac{11}{20}$ work will be done by $B$ in $(\dfrac{11}{20} \times 20)$ days $=11$ days.

Hence, the remaining work is done by $B$ in 11 days.

## Practice Questions

Here are practice questions related to work done, through which it can be made in a better way:

Q1. In 300 days, Sanjay finished the school project. If Piyush is 50% more productive than Sanjay, how many days will it take him to finish the identical task?

Ans. 200

Q2. A task can be completed by Sourav and Anshu in 18 days. Anshu and Himanshu can do it in 24 and Sourav and Himanshu can do it in 36 days, respectively. How many days will it take Sourav, Himanshu, and Anshu to complete the task if they collaborate?

Ans. 16 Days

Q3. In 600 days, Sanjay finished the school project. If Piyush is 20% more productive than Sanjay, how many days will it take him to finish the identical task?

Ans. 500

Q4. Piyush, Santosh, and Ramesh are hired as construction workers by a builder on one of his projects. They finish a piece of work in 20, 30, and 60 days, respectively. If Santosh and Ramesh help Piyush every third day, how many days will it take him to do the entire task?

Ans. 15 Days

Q5. A project that Santosh and Prajapati are working on can be finished in 30 days. Santosh put in 16 days of labour, and Prajapati took 44 days to finish it all. How many days would it have taken Prajapati to do the entire project on her own?

Ans. 60 Days

## Summary

In this article, we discussed the topic of time and work. Time and work are related concepts. Time is a unit of time, work is an activity done in a given time. Time and work are very important in the field of mathematics. This is because it helps them understand the concept of time and how it can be used to solve mathematical equations. The amount of work you do is related to the amount of time you spend on it. We have understood the topic of time and work perfectly by using some solved problems on work done and time spent.

## FAQs on Work Done Problems

1. What does the term "word problems" mean?

Word problems are defined as mathematical problems that are written in an ordinary language rather than mathematical terms and symbols.

2. What are some of the different work done problems?

Problems based on Painting and Pipes, Tubs and Man-Hours, Unequal Times Etc. are some of the different work done problems.

3. Are time and work directly or inversely correlated?

The relationship between time and work is directly correlated. As a result, more work may be done in more time, and vice versa.