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A and B together can complete a work in 15 days while B and C together can complete the same work in 20 days. A worked for 8 days, then B worked for 10 days and C completed the remaining work in 3 days. In how many days C can complete the whole work alone?

A and B together can complete a work in 15 days while B and C together can complete the same work in 20 days. A worked for 8 days, then B worked for 10 days and C completed the remaining work in 3 days. In how many days C can complete the whole work alone? Correct Answer 30/11

Given:

Time to complete the work by A and B together = 15 days

Time to complete the work by B and c together = 20 days

A worked = 8 days

B worked = 10 days

C worked = 3 days

Calculations:

Let the total work be (LCM of 15 and 20) 60 units.

1 day work of A and B together = 60/15

⇒ 4 units

1 day work of B and C together = 60/20

⇒ 3 units

A × 8 + B × 10 + C × 3 = 60 units

⇒ A × 8 + B × (8 + 2) + C × (2 + 1) = 60

⇒ 8A + 8B + 2B + 2C + C = 60

⇒ 8(A + B) + 2(B + C) + C = 60

⇒ 8(4) + 2(3) + C = 60

⇒ 32 + 6 + C = 60

⇒ 38 + C = 60

⇒ C = 22 units/day

Time taken by C to complete whole work = 60/22

⇒ 30/11 days

∴ C can complete the whole work alone in 30/11 days

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