A can do a piece of work in 28 days, while B can do the same piece of work in 42 days. They begin working together and 6 days before completion of work, A leaves. Find the total number of days taken to complete the work.

Suppose the work finished in x days. A' s one day work is 1/28 day B's one day work is 1/42 day According to the question, Let the total work was done in x days then, A works for (x - 6)days Then, (x - 6)/28 + x/42 = 1 3x – 18 + 2x = 84 5x = 102 x = 102/5 days. Alternate Method: A B 28 42 let total work = LCM of 28 & 42 = 84 units So Eff : 3 : 2 So in last 6 days B worked alone so his work in last 6 days = 2`xx` 6 = 12 units So remaining work = 84-12 = 72 units Hence A & B will do it in = 72/5days Hence total days = 72/5 +6 = 102/5 days

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