Question

A can do a piece of work in 10 days and B alone can do it in 14 days. How many days will be required by both together to finish the work?

Answer 1

A's 1 day work=1/10
B's 1 day work=1/14
(A+B)'s 1 day work=1/10+1/14=6/35
so they finish the work in 35/6 days

Answer 2

Hi.

Here is your answer-

Time taken by A to complete the piece of work = 10 days
Thus, A's one day work = 1/10 days

Time taken by B to complete the piece of  work = 14 days
Thus, B's one day work = 1/14 days

Now,
(A +B)'s one day work = (1/10 + 1/14)
                                    = ({7 + 5} /70)               [Taking L.C.M.]
                                    = (12/70)
                                    = 6/35 days

Thus, the total time taken by A and B together to complete the work = 35/6  days.

Hope it helps.

Have a nice day.

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