Question

Ajit can do a certain work in 24 days. Bharath can do the same work in 30 days. When Chandra joins them and they do the work together, they complete the work in 12 days. Find out the time required by Chandra to complete the work alone

• A. 100 days
• B. 125 days
• C. 130 days
• D. 120 days

Answer 1

The correct option is D 120 days

In one day Ajit can do $\left(\frac{100}{24}\right)\%$ of the work.

In one day Bharath can do $\left(\frac{100}{30}\right)\%$ of the work.

Working together they can do $\left(\frac{100}{24}\right)\%+\left(\frac{100}{30}\right)\%=7.5\%$ of the work in one day.

Now when Chandra joins them, they complete the work in 12 days Ajit, Bharath and Chandra together complete $\left(\frac{100}{12}\right)\%$ of the work in a day.

Now, Ajit and Bharath do $7.5\%$ of the work in a day.

Ajit, Bharath and Chandra do $\left(\frac{100}{12}\right)\%$ of the work in a day.

Chandra can do $(\frac{100}{12}-7.5)\%=\left(\frac{10}{12}\right)\%$ of the work in a day.

So, to complete $100\%$ of the work, Chandra will take $\left[\frac{100}{\left(\frac{10}{12}\right)}\right]$= 120 days. Hence option (e).

2nd method:- In 12 days ajit completes $\frac{12}{24}$ i.e $50\%$ and Bharat completes $\frac{12}{30}$ i.e $40\%$ , then chandra completes $(100-90)=10\%$ work in 12 days. Then he will take 120 days to complete full work.