Dear Reader, The problem we are going to see today is from “Time and Work”. You must remember a principle regarding work and the number of people involved. When the number of people doing a work increase, the time to complete the work will decrease proportionately and vice versa.

For example, If 10 people can build a wall in 20 days, 20 people will take just 10 days to complete the same work. In recent PO exams, there were questions based on this relationship. Below example will help you understand better.

**Example Question:** 40 men can do a work in 4 days and 30 women can do the work in 3 days. If 10 men work for the first five days and 10 women work for the next five days, how much work will be left behind (remaining)?

**Step 1:** Work done by 10 men in 5 days

40 men can do the work in 4 days.

10 men is 1/4th of 40 men.

Since work is **inversely proportional** to number of people,

**1/4th** of 40 men will take **4 times** the number of days taken by 40 men.

We know 40 men take 4 days to complete.

Therefore, 10 men (1/4 of 40) will take (4 x 4 =) 16 days to complete.

Therefore, work done by 10 men in 1 day = 1/16

Work done by 10 men in 5 days = 5 x 1/16 = 5/16 … equation (1)

**Step 2:** Work done by 10 women in 5 days

30 women can do the work in 3 days.

10 women is 1/3rd of 30 women.

**1/3rd** of 30 women will take **3 times** the number of days taken by 30 women.

We know 30 women take 3 days to complete.

Therefore, 10 women (1/3rd of 30) will take (3 x 3) = 9 days to complete.

Therefore, work done by 10 women in 1 day = 1/9

Work done by 10 women in 5 days = 5 x 1/9 = 5/9 … equation (2)

**Step 3:** Remaining Work

To find the leftover work, we have to add the values in equations 1 and 2 and subtract it from 1. (‘1’ represents full work)

Remaining Work = 1 – (5/16 + 5/9)

= 1 – ((5 x 9 + 5 x 16) /144)

= 1 – 125/144

= 19/144

Therefore, our answer is 19/144