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C is 5 times as productive as B. A takes 60 days to complete a task. If A, B and C work together they can complete the task in 12 days. In how many days can B complete the task if he worked alone?
- A18
- B27
- C90
- D72
Answer not set
Discussion 1
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CCommunity
Let the total work = 60 (LCM of 60 & 12)
⇒ Efficiency of A = 60/60 = 1
⇒ Efficiency of (A + B + C) = 60/12 = 5
Since C is 5 times as productive as B, efficiency of C will be 5 times of the efficiency of B.
Let efficiency of B be n then efficiency of C will be 5n,
⇒ 1 + n + 5n = 5
⇒ 6n = 4
⇒ n = 2/3
⇒ Efficiency of B = 2/3
Time taken by B alone to complete the task = 60/(2/3) = 90 days
⇒ Efficiency of A = 60/60 = 1
⇒ Efficiency of (A + B + C) = 60/12 = 5
Since C is 5 times as productive as B, efficiency of C will be 5 times of the efficiency of B.
Let efficiency of B be n then efficiency of C will be 5n,
⇒ 1 + n + 5n = 5
⇒ 6n = 4
⇒ n = 2/3
⇒ Efficiency of B = 2/3
Time taken by B alone to complete the task = 60/(2/3) = 90 days