A piece of work can be complete by P and Q together in 24 days, and the same piece of work can be completed by R alone in 60 days. If P and R together can do the same work in 36 days, then find the time taken by Q to complete this piece of work alone.

$32 \frac{8}{11}$ days

P + Q = 24 days,

R = 60 days,

P + R = 36 days,

⇒ P + R = 10  (Efficiency)

⇒ P + 6 = 10

⇒ P = 4,

Similarily,

⇒ P + Q = 15,

⇒ 4 + Q = 15,

⇒ Q = 11, 

Therefore, time required by Q to complete work alone = \(\frac{360}{11}\) = \( { 32}_{ 11}^{ 8} \) days,     ..(\(\frac{Work}{Efficiency}\) = Time)