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A and B together completes a task in 10 days, B and C together completes in 15 days and A and C together completes in 18 days. In how many days, A, B and C together finish the task?

A and B together completes a task in 10 days, B and C together completes in 15 days and A and C together completes in 18 days. In how many days, A, B and C together finish the task? Correct Answer 9 days

Given:

A and B together completes the task in 10 days

B and C together completes the task in 15 days

A and C together completes the task in 18 days

Formula used:

Efficiency = Work/(Time Taken)

Calculation:

Total task = LCM of 10, 15 and 18 = 90 units

Efficiency of (A + B) = (90/10) = 9 units/day

Efficiency of (B + C) = (90/15) = 6 units/day

And Efficiency of (A + C) = (90/18) = 5 units/day

Now, (A + B) + (B + C) + (A + C) = 9 + 6 + 5

⇒ 2(A + B + C) = 20

⇒ (A + B + C) = 10 units/day

Time taken by (A + B + C) to complete the task = (90/10) = 9 days

∴ A, B and C together finish the task in 9 days.

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