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?

Let P, Q & R take a, b & c days to complete the work individually.

Given, p & Q can do piece of work in 40 days.

=> 1/a + 1/b = 1/40

Given, Q & R can do it in 120 days.

=> 1/b + 1/c = 1/120

Given, b = 180 days

=> 1/c = 1/120 - 1/180

=> 1/a = 1/40 - 1/180

The work done by P & R in one day = 1/a + 1/c

= (1/40 - 1/180) + (1/120 - 1/180)

= 1/40 + 1/120 - 1/90

= (9+3-4)/360

= 8/360

= 1/45

=> The number of days P & R will take to do the piece of work together is 45 days.

C is correct choice.