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A and B together work for 3 days, B then worked alone for 2 days, A then worked alone for 3 days and the work was finished. If A works for 8 days alone and B works for 4 days alone, the work will be finished. How many days will A alone work if B works for 5 days alone?

A and B together work for 3 days, B then worked alone for 2 days, A then worked alone for 3 days and the work was finished. If A works for 8 days alone and B works for 4 days alone, the work will be finished. How many days will A alone work if B works for 5 days alone? Correct Answer 6

Given:

A and B together work for 3 days, B then worked alone for 2 days, A then worked alone for 3 days and the work was finished.

If A works for 8 days alone and B works for 4 days alone, the work will be finished.

Calculation:

Let the work done by A, B and C in a day be A, B and C respectively.

Given, 3(A + B) + 2B + 3A = 1

Or, 6A + 5B = 1

Also, 8A + 4B = 1

Equating the two equations, we get,

⇒ 6A + 5B = 8A + 4B

Or, B = 2A

Capacity B / A = 2 / 1

So, Total work = 6A + 5B = 6 × (1) + 5 × (2) = 16 units

Let A alone work for N days

⇒ N × A + 5B = 16

⇒ N × (1) + 5 × (2) = 16

⇒ N = 6 days

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