Three people P, Q and R have been assigned a work. P and Q can complete a work in 15 days and Q and R can complete a work in 18 days and all of them can complete the whole work in 12 days, then find the number of days in which P and R alone can do the whole work?

Option 1 : P = 36 days, R = 60 days

Given:

P, Q and R can do the whole work in 12 days

P and Q can complete the same work in 15 days

Q and R can complete the same work in 18 days

Assumption:

Let the total work be 180 units (LCM of 12, 15 and 18)

Calculation:

⇒ 1 day work of P and Q = 12 units        ---- 1

⇒ 1 day work of Q and R = 10 units         ---- 2

⇒ 1 day work of P, Q and R = 15 units        ---- 3

From equation 1 and 3,

⇒ R’s 1 day work = 3

From equation 2 and 3,

⇒ P’s 1 day work = 5

∴ P alone can do the whole work in 180/5 = 36 days and R alone can do the whole work in 180/3 = 60 days.