Abhishek and Deepanshi undertake to do a piece of work for Rs. 1,000. Abhishek alone can do it in 5 days and Deepanshi alone can do it in 10 days. With the help of Chitransh, they finish it in 2 days. How much should Chitransh be paid for his contribution?

Correct option is D

Given:
Total payment for the work = Rs. 1,000
Abhishek can complete the work alone in 5 days
Deepanshi can complete the work alone in 10 days
All three (Abhishek, Deepanshi, and Chitransh) finish the work together in 2 days
Formula Used:
1-day work = 1 / Time taken individually
Payment share = Work share × Total amount
Solution:
Abhishek’s 1-day work = $$\frac{1}{5}$$​
Deepanshi’s 1-day work = $$\frac{1}{10}$$​
Let Chitransh’s 1-day work = x
Together in 1 day

$$\begin{aligned}&\frac{1}{5} + \frac{1}{10} + x = \frac{1}{2} \\&\Rightarrow \frac{2 + 1}{10} + x = \frac{1}{2} \\&\Rightarrow \frac{3}{10} + x = \frac{1}{2} \\&\Rightarrow x = \frac{1}{2} - \frac{3}{10} \\&\Rightarrow x = \frac{5 - 3}{10} = \frac{2}{10} = \frac{1}{5}\end{aligned}$$​​
Chitransh’s 1-day work =$$\frac 15$$​
In 2 days, Chitransh’s work = 2 × $$\frac 15= \frac 25$$​
Chitransh’s share in payment = $$\frac 25$$​ × 1000 = Rs. 400