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.
Answer & explanation
Correct answer: option 4
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)