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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?

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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?
1). 18
2). 27
3). 90
4). 72


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1 answers

44 vote
Answered by on | Votes 44 |

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
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