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 = $9+\frac{36}{60}=9\frac{3}{5}=\frac{48}{5}$ hours.
Work of (A + B) in 1 hour = $\frac{5}{48}$
Work of C in 1 hour = $\frac{1}{48}$
Work of (A + B + C) in 1 hour = $\frac{5}{48}+\frac{1}{48}=\frac{1}{8}$ -------(1)
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) = $\frac{1}{8}$
⇒ 1 hour work of A = $\frac{1}{8×2}=\frac{1}{16}$
1 hour work of B = $\frac{5}{48}–\frac{1}{16}=\frac{5–3}{48}$
⇒ 1 hour work of B = $\frac{2}{48}=\frac{1}{24}$
So, B alone will complete the work in 24 hours.
Hence, the correct answer is 24 hours.
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