P can work thrice as fast as Q. Working independently, Q can complete a task in 24 days. In how many days can P and Q together finish the same task?

6

Given,

P can work thrice as fast as Q, therefore,

P : Q = 3 : 1 (Efficiency)

P : Q = 1 : 3 (time)

⇒ Q worked 24 days

So, 3R = 24

1R = 8

⇒ P complete the work in 8 days

Let total work = 24 units ( LCM of 8 and 24 )

⇒ Time required by P + Q to complete the work = \(\frac{24}{3+1}\) = \(\frac{24}{4}\) = 6 days,  ..(\(\frac{Work}{Efficiency}\) = Time)