Radha and Shama undertake a piece of work for ₹36,000. Radha can do it in 20 days and Shama can do it in 60 days. With the help of Rama, they finished it in 10 days. How much should Rama be paid for her contribution?

Correct option is C

Given:

Radha can complete the work in 20 days

Shama can do the same work in 60 days

They completed the work in 10 days

Total payment for the work = ₹36,000  

Concept Used:

The payment should be divided among Radha, Shama, and Rama based on their respective contributions to the total work.

Formula Used:

Let total work be 1.

Then, work done in 1 day =$$\frac{1}{Total\ time\ to\ work}$$ 

Solution:

Radha’s one day’s work =  $$\frac{1}{20}$$​​

Shama’s one day’s work = $$\frac{1}{60}$$​​

Radha and Shama’s one day work = $$\frac{1}{20}+\frac{1}{60}= \frac{3+1}{60}=\frac{1}{15}$$​​

Radha and Shama’s 10 days work =$$\frac{1}{15}\times 10 = \frac{10}{15} =\frac{2}{3}$$​​

Remaining work $$1- \frac{2}{3} =\frac{1}{3}$$​​

So,  Rama did $$\frac{1}{3}$$​rd of work

Rama be paid$$\frac{1}{3}$$rd of 36000 = $$\frac{1}{3} \times 36000$$​ = ₹12000