Vicky can complete a piece of work in 40 days. He worked for 8 days, then Gurpreet Singh finished it in 32 days. In how many days can Vicky and Gurpreet Singh together complete the work?

Correct option is B

Given:

Vicky alone can complete the work in 40 days.

Vicky worked for 8 days, then Gurpreet Singh finished the remaining work in 32 days.

We need to find in how many days Vicky and Gurpreet Singh together can complete the work.

Concept Used:

Work done per day by a person is given by:

​$$\text{Work Rate} = \frac{1}{\text{Total Days Required}}$$​​

Total time to complete the work together is:

​$$\text{Total Time} = \frac{1}{\text{Total Work Rate}}​$$​​

Solution:

Work done by Vicky in 8 days:

​$$\text{Vicky's daily work rate} = \frac{1}{40}$$​​

​$$\text{Work done in 8 days} = 8 \times \frac{1}{40} = \frac{8}{40} =\frac{1}{5} ​$$​​

So, remaining work

$$1 - \frac{1}{5} = \frac{4}{5}$$​​

Work rate of Gurpreet Singh:
Gurpreet Singh completed $$\frac{4}{5}$$​​ of the work in 32 days, so his daily work rate is:

​$$\frac{\frac{4}{5}}{32} = \frac{4}{160} = \frac{1}{40}$$​​

So, Gurpreet Singh’s daily work rate =$$\frac{1}{40}$$​​

Combined Work Rate of Vicky and Gurpreet Singh:

​$$\frac{1}{40} + \frac{1}{40} = \frac{2}{40} = \frac{1}{20}​$$​​

So, Vicky and Gurpreet Singh together complete $$\frac{1}{20}$$​ of the work per day.

Total time to complete the work together:

​$$\text{Total Time} = \frac{1}{\frac{1}{20}} = 20$$ days

Option (b) is right.