Question

A, B and C can finish a work in 10, 20 and 60 days respectively. C work for 5 days and is joined by A for another 5 days, then A leaves and B joins C. In how many days will the work be finished?
1. 16
2. 12
3. 14
4. 15

Answer 1

Correct Answer - Option 4 : 15

Given:

 A, B and C can finish a work in 10, 20 and 60 days respectively. C work for 5 days and is joined by A for another 5 days, then A leaves and B joins C.

Formula:

 If A and B can together finish it in t days with A and B finishing the work in a and b days respectively,

1/a + 1/b = 1/t

Calculation:

Let total work be 60 units, let efficiency of A, B and C be A, B and C only.

A’’s capacity = 60/10 = 6

B’s capacity = 60/20 = 3

C’s capacity = 60/60 = 1

Let at then end B and C together takes n days.

ATQ,

5C + 5(C + A) + n (B + C) = 60

⇒ 5 × 1 + 5(1 + 6) + n (3 + 1) = 60

⇒ 5 + 35 + 4n = 60

⇒ 4n = 20

⇒ n = 5

Total time taken to finish = 5 + 5 + 5 = 15 days.