Water filled by first pipe in 1 min $=\frac{1}{12}$

Water filled by second pipe in 1 min $=\frac{1}{15}$

Water filled by both the pipes in 5 min $=5\left(\frac{1}{12}+\frac{1}{15}\right)=\frac{3}{4}$

Water filled when all the three pipes work together in 1 min $=\left(\frac{1}{12}+\frac{1}{15}\right)-\frac{1}{6}=-\frac{1}{60}$

Here negative sign implies that $\frac{1}{60}$^th part is emptied in 1minute

 ∴ $\frac{3}{4}$^th part is emptied in $60\times \frac{3}{4}=45 \mathrm{minutes}$

Hence option B is correct.