Question

A, B, and C together can finish a piece of work in 12 days. A and C together work twice as much as B, and A and B together work thrice as much as C. In what time (in days) could each do it separately?

(a) A: 20, B: 60, C: 30
(b) A: 30, B: 20, C: 60
(c) A: 15, B: 45, C: 30
(d) A: 18, B: 36, C: 24

Answer 1

A, B, and C can complete the work separately in 18, 36, and 24 days respectively.

Step-by-step explanation:

To solve this problem, let's assign the following variables:

A = the amount of work A can do in 1 day

B = the amount of work B can do in 1 day

C = the amount of work C can do in 1 day

From the given information, we can form the following equations:

1) A + B + C = 1/12 (since they can complete the work together in 12 days)

2) A + C = 2(B) (A and C together work twice as much as B)

3) A + B = 3(C) (A and B together work thrice as much as C)

Solving these equations, we can find the values of A, B, and C:

A = 18, B = 36, C = 24

Therefore, each person can complete the work separately in the following times:

A: 18 days

B: 36 days

C: 24 days