Question:
Tick (✓) the correct answer:
A alone can do a piece of work in 10 days and B alone can do it in 15 days. In how many days will A and B together do the same work?
(a) 5 days
(b) 6 days
(c) 8 days
(d) 9 days
Solution:
(b) 6 days
A can do a work in 10 days.
A's 1 day work $=\frac{1}{10}$
B can do a work in 15 days.
B's 1 day work $=\frac{1}{15}$
$(\mathrm{A}+\mathrm{B})$ 's 1 day work $=\frac{1}{10}+\frac{1}{15}=\frac{5}{30}=\frac{1}{6}$
$\mathrm{A}$ and $\mathrm{B}$ together will take 6 days to complete the work.