A work is done by P & Q, Q & R, and R & P in 12, 15, and 20 days, respectively. How many days will P alone take to complete the work?

30 days

P + Q = 12 days,

Q + R = 15 days,

R + P = 20 days,

⇒ Adding all the efficiencies, we get,

⇒ 2(P + Q + R) = 12

⇒ P + Q + R = 6,

Therefore P = 2 (Efficiency)

⇒ Time taken by P to complete the total work = \(\frac{60}{2}\) = 30 days.

..(\(\frac{Work}{Efficiency}\) = Time)