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?
Answer & explanation
Correct answer: option 3
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)