B and C together can complete a work in 8 days A and B and A and C together can complete the same wo...........

Quant (SSC) Time and work

B and C together can complete a work in 8 days. A and B, and A and C together can complete the same work in 12 days and 16 days respectively. In how many days can A, B and C together complete the same work?

3 9/13 days

7 5/13 days

7 5/12 days

3 5/12 days

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Explanation:

(A + B + C) together finish the work in
[2xyz / xy + yz + zx] days
A and B together finish a piece work = x = 12 days
B and C together finish a piece work = y = 8 days
C and A together finish a piece work = z = 16 days
By the short trick approach:
A, B and C can do the work in
= 2 × 12 × 8 × 16 /12 × 8 + 8 × 16 + 16 × 12 days
After taking 8 as a common term we get,
= 2 × 12 × 16 /12 + 16 + 24 days
After taking 4 as a common term we get,
= 2 × 3 × 16 /3 + 4 + 6 days = 96/13 = 7 5/13 days