Two pipes A and B can fill an empty tank in 30 minutes and 40 minutes respectively. Both pipes are opened together and after t minutes the pipe B is closed. If the tank gets completely filled in 21 minutes then t is equal to:

12

The correct answer is Option (1) → 12

$\text{Rate of A}=\frac{1}{30},\ \text{Rate of B}=\frac{1}{40}$

$\text{For } t \text{ minutes: work done} = t\left(\frac{1}{30}+\frac{1}{40}\right)=t\cdot\frac{7}{120}$

$\text{Remaining time} = 21 - t,\ \text{only A works}$

$\text{Work done} = \frac{21 - t}{30}$

$t\cdot\frac{7}{120} + \frac{21 - t}{30} = 1$

$\frac{7t}{120} + \frac{4(21 - t)}{120} = 1$

$\frac{7t + 84 - 4t}{120} = 1$

$\frac{3t + 84}{120} = 1$

$3t + 84 = 120 \Rightarrow 3t = 36 \Rightarrow t = 12$

$t = 12\ \text{minutes}$