A can finish a piece of work in 20 days and B can finish it in 24 days. They work together for 10 days then A leaves. In how many days will B finish the remaining work?

Correct option is D

Given:

A can finish the work in 20 days.

B can finish the work in 24 days.

A and B work together for 10 days, and then A leaves.

Solution:

Rate of work of A $$= \frac{1}{20}$$​​

Rate of work of B $$= \frac{1}{24}$$​​

Combined rate =$$\frac{1}{20} + \frac{1}{24}$$​

Combined rate =$$\frac{6}{120} + \frac{5}{120} = \frac{11}{120}$$​

So, A and B together can complete $$\frac{11}{120}$$​ of the work per day.

In 10 days, A and B will complete:

Work done in 10 days = $$10 \times \frac{11}{120} = \frac{110}{120} = \frac{11}{12}$$​

Remaining work after 10 days.

Remaining work =$$1 - \frac{11}{12} = \frac{1}{12}$$​

Since B's rate of work is $$\frac{1}{24}$$​ per day, the time B will take to finish the remaining $$\frac{1}{12}$$​ of the work is:

Time = $$\frac{\frac{1}{12}}{\frac{1}{24}} = \frac{1}{12} \times \frac{24}{1} = 2 \, \text{days}$$​

Alternate Method:

Total Work = 120 Unit 

​A and B work together for 10 days

Work Done in 2 Days = 6 + 5 = 11 

11 $$\times$$ 10 = 110 Unit  

Remaining work = 120 - 110 = 10 Unit  

A and B work together for 10 days, and then A leaves.

So, B complete remaining work 

Time = $$\frac {10}{5}=2$$ days​