P and Q can do a piece of work in 40 days. Q and R can do it in 120 days. Q alone could finish it in 180 days. In how many days will P and R working together finish the work?

Correct option is D

Given:

P and Q together complete the work in 40 days.

Q and R together complete the work in 120 days.

Q alone completes the work in 180 days.

Formula Used:

​$$Work \ done \ in \ one \ day = \frac{1 }{Number \ of\ days \ to\ complete \ the \ work}$$​​

Solution:

Let the total work be 1 unit.

Work done by Q in 1 day = $$\frac{1}{180}$$​​

Work done by P and Q in 1 day = $$\frac{1}{40}$$​​

Work done by Q and R in 1 day = $$\frac{1}{120}$$​

Work done by P in 1 day = $$\frac{1}{40} - \frac{1}{180} = \frac{9 - 2}{360} = \frac{7}{360}$$​​

Work done by R in 1 day = $$\frac{1}{120} - \frac{1}{180} = \frac{3 - 2}{360} = \frac{1}{360}$$​​

Work done by P and R in 1 day = $$\frac{7}{360} + \frac{1}{360} = \frac{8}{360} = \frac{2}{90}$$​​

\text{Number of days required by P and R} = $$\frac{1}{\frac{2}{90}} = 45$$​​

Hence, P and R together will finish the work in 45 days.