Three pipes A, B and C can fill a tank in 6 hours, 9 hours and 12 hours respectively. B and C are opened for half an hour, then A is also opened. The time taken by the three pipes together to fill the remaining part of the tank is -

A. 3 hours

B. 2 hours

C. $${\text{2}}\frac{1}{2}$$ hours

D. $${\text{3}}\frac{1}{2}$$ hours

Answer: Option C

Solution(By Examveda Team)

In half an hour (B + C) must have filled
$$ = \frac{4}{2} + \frac{3}{2} = \frac{7}{2}\,{\text{units}}$$
Capacity left
$${\text{ = 36}} - \frac{7}{2} = \frac{{65}}{2}\,{\text{units}}$$
Now all pipes will fill the remaining tank
$$\eqalign{ & {\text{ = }}\frac{{65}}{{2 \times \left( {6 + 4 + 3} \right)}} \cr & = \frac{{65}}{{2 \times 13}} \cr & = \frac{5}{2} \cr & = 2\frac{1}{2}\,{\text{hours}} \cr} $$