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
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