A and B can do a work in 9 days and 12 days respectively. If they work on alternate days starting with A, then in how many days will the work be completed?

$10\frac{1}{4}$ days

We have,

A = 9 days

B = 12 days

Total work = L.C.M of A and B

Total work = 36

Work done by A in one day = \(\frac{36}{9}\) = 4

Work done by B in one day = \(\frac{36}{12}\) = 3

Now, according to the question,

4 + 3 = 7 work done in two days.

Days              Work

2                     7

5(2                 7)5

---------------------

10                  35

Remaining (36 - 35 = 1) work is done by A with 4 efficiency

Time taken by A and B to finish the work = 10\(\frac{1}{4}\)days