Question
A is 60% as efficient as B, and C is 50% as efficient as
A. If A, B, and C working together can finish a task in 15 days, how many days will it take for B to complete the same task on his own?
Solution
Let B’s efficiency be 1 unit/day. Then, A’s efficiency = 0.6 units/day and C’s efficiency = 0.5 × 0.6 = 0.3 units/day. Combined efficiency of A, B, and C = 0.6 + 1 + 0.3 = 1.9 units/day. They can complete the work in 15 days, so total work = 1.9 × 15 = 28.5 units. Time taken by B to complete the work alone = Total work ÷ B’s efficiency = 28.5 ÷ 1 = 28.5 days. Final Answer: (c) 28.5 days
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