Question : A can do as much work as B and C together can do, A and B can do a piece of work in 9 hours 36 minutes and C can do it in 48 hours. The time (in hours) that B needs to do the work alone, is:
Option 1: 18 hours
Option 2: 24 hours
Option 3: 30 hours
Option 4: 12 hours
Correct Answer: 24 hours
Solution :
9 hours 36 minutes =
Work of (A + B) in 1 hour =
Work of C in 1 hour =
Work of (A + B + C) in 1 hour =
According to the given condition,
1 hour work of A = 1 hour work of (B + C) --------------(2)
From equations (1) and (2),
⇒ 2 × (1 hour work of A) =
⇒ 1 hour work of A =
1 hour work of B =
⇒ 1 hour work of B =
So, B alone will complete the work in 24 hours.
Hence, the correct answer is 24 hours.