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B and C together can complete a work in 8 days, A and B together can complete the same work in 12 days, and A and C together can complete the same work in 16 days. In how many days can A, B and C together completes the work?Options3.6923076927.3846153857.4166666673.416666667

Question

B and C together can complete a work in 8 days, A and B together can complete the same work in 12 days, and A and C together can complete the same work in 16 days. In how many days can A, B and C together completes the work?Options3.6923076927.3846153857.4166666673.416666667

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Solution

The problem can be solved using the concept of work and time.

Step 1: Find the work done by A, B, and C in one day.

We know that B and C can complete the work in 8 days, so the work done by B and C in one day is 1/8.

Similarly, the work done by A and B in one day is 1/12, and the work done by A and C in one day is 1/16.

Step 2: Add the work done by the pairs in one day.

(Work done by B and C) + (Work done by A and B) + (Work done by A and C) = (1/8) + (1/12) + (1/16) = 1/4

Step 3: Divide the total work done by the pairs in one day by 2 to get the work done by A, B, and C in one day.

(Work done by A, B, and C in one day) = (1/4) / 2 = 1/8

Step 4: The time taken by A, B, and C to complete the work is the reciprocal of the work done by them in one day.

So, the time taken by A, B, and C to complete the work = 1 / (1/8) = 8 days

Therefore, A, B, and C together can complete the work in 8 days.

This problem has been solved

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