A is thrice as efficient as B and hence completes a work in 40 days less than the number of days taken by B. What will be the number of days taken by both of them when working together?

The correct option is B

15 days

Let efficiency of B be x
Days are inversely proportional to efficiency.
According to question:
$\Rightarrow 3x-x=40\Rightarrow 2x=40\therefore x=20$
Time taken by A = x days = 20 days
Time taken by B = 3x days = $3\times 20=60days$
Time taken by A and B together $=\frac{20\times 60}{80}=15days$