2 men can do a peice of work in 6 hours and 4 hours respectively. After the first has worked for 2 hours' he is joined by the other. By when should the work be compleated?

Let two men are A and B.

Given: A can do a piece of work in 6 hours and B can do in 4 hours. Thus,

A’s 1 hour work = 1/6

And, B’s 1 hour work = 1/4

And, (A+B)’s 1 hour work = 1/6 + 1/4 = 5/12

After the first has worked for 2 hours ' he is joined by the other, so,

(A)’s 2 hour work = 2(1/6) = 1/3

Remaining work = 1-1/3 = 2/3

Since, 5/12 work is done by (A+B) in 1 hrs

Therefore, 2/3 work is done by (A+B) in 12/5 × 2/3 = 8/5 hrs

Therefore,

Total time to be completed the work = 2 + 8/5 = 18/5 = 3 hrs.

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