Question

A alone can complete a work in 16 days and B alone in
12 days. Starting with A, they work on alternate days.
The total work will be completed in:
​

Answer 1

work done by the 'A'in one day = 1/16 = 3/48

work done by the 'B'in one day = 1/12 = 4/48

(48 = lcm(12, 16))

Assuming the work divided into 48 parts, the amount of work completed each day forms the series 3, 4, 3, 4, 3, 4, .

In 12 days, 42 parts will be finished

In 13 days, 45 parts will be finished

In 14 days, 49 parts will be finished

But since there is only 48 parts of the work,

the work will be finished in 13.75 days.

Since number of days should be integer, it means answer is 14 days.