P can do a piece of work in 40 days. He worked on it for 10 days and then Q finished the work in 30 days. In how many days can P and Q together finish the work?

P’s 1 day work
$= \frac{1}{40}$
Work done by P in 10 days
$= \frac{10}{40}$
$= \frac{1}{4}$
Remaining work
$= 1 - \frac{1}{4}$
$= \frac{3}{4}$
Q finishes $\frac{3}{4}$ work in 30 days.
So, Q’s 1 day work
$= \frac{3}{4 \times 30}$
$= \frac{1}{40}$
Now,
P’s 1 day work $= \frac{1}{40}$
Q’s 1 day work $= \frac{1}{40}$
Together,
$= \frac{1}{40} + \frac{1}{40}$
$= \frac{1}{20}$
Therefore, time taken together= 20 days
Correct Answer: 20 days