Question

A alone can complete the work in 12 days and B alone can complete in 24 days. In how many days A and B can complete the work together?

Answer 1

A can do the piece of work in 12 days.
One day work of A=1/12
B can complete the work in 24 days.
One day work of B=1/24

(A+B)'s one day work=
$= \frac{1}{12} + \frac{1}{24} \\ = \frac{2 + 1}{24} \\ = \frac{3}{24} \\ = 8$
Hence,they can together complete it in 8 days..

Answer 2

A can complete the work in 12 days
A works
$\frac{1}{12}$
in a day
such that B works 1/24 in a day

when they works togethor
$\frac{1}{12 } + \frac{1}{24 } = \frac{2}{24} + \frac{1}{24} = \\ \frac{3}{24} = \frac{1}{8}$
they will take 8 days to complete the work