P, Q, and R can do a job in 12 days together. If their efficiency of working be in the ratio 3 : 8 : 5, Find in what time Q can complete the same work alone?

Question: P, Q, and R can do a job in 12 days together. If their efficiency of working be in the ratio 3 : 8 : 5, Find in what time Q can complete the same work alone.

Solution:
Given the ratio of efficiencies of P, Q & R are 3 : 8 : 5
Let, the efficiencies of P, Q & R be 3x, 8x and 5x respectively

They can do work for 12 days.
⇒ Total work = 12 × 16x = 192x


∴ The required time taken by Q to complete the job alone = 192x/8x
= 24 days.