X is 3 times as fast as Y and is able to complete the work in 40 days less than Y. Then the time in which they can complete the work together is

Let the number of days taken by Y to complete the work be "a".
Since X is three times as fast as Y Work completed per day by X is given by
$$\frac{1}{X} = \frac{3}{Y}$$
$$a \frac{1}{Y} =1$$ -------------- 1
Since X takes 40 days less time than Y
$$(a-40) \frac{1}{X} =1$$ ----------------- 2
Replacing $$\frac{1}{X}$$ in 2 and solving for "a" we get
a=60 days.
Substituting a in 1 and 2 we get
$$\frac{1}{X} = \frac{1}{20}$$
$$\frac{1}{Y} $$$$= \frac{1}{60}$$
Let the number of days it takes when both X and Y are working together be $$n$$.
$$ n \times ( \frac{1}{X} + \frac{1}{Y}) =1 $$
$$ n \times ( \frac{1}{20} + \frac{1}{60}) =1 $$
$$n=15$$
Hence Option A is the correct answer.