Correct Answer: 10 days

Explanation:

A, B & C takes 2 days to complete = 1 work

A, B & C takes 1 days to complete =$\frac{1}{2}$
$\frac{1}{2}$
work

The rest of work = 1- $\frac{1}{2}$
$\frac{1}{2}$
= $\frac{1}{2}$
$\frac{1}{2}$

Only B takes 5 days to complete = 1 work

Only B takes 1 days to complete =$\frac{1}{5}$
$\frac{1}{5}$
work

Only C takes 4 days to complete = 1 work

Only C takes 1 days to complete =$\frac{1}{4}$
$\frac{1}{4}$
work

Jointly (B + C) can do in 1 day = $\frac{1}{5}$
$\frac{1}{5}$
+ $\frac{1}{4}$
$\frac{1}{4}$
=$\frac{9}{20}$
$\frac{9}{20}$

A can do $\frac{1}{20}$
$\frac{1}{20}$
work in = 1 day

A can do 1 work in = 20 day

A can do $\frac{1}{2}$
$\frac{1}{2}$
work in = $\frac{20}{2}$
$\frac{20}{2}$
= 10 days