Three pipes A, B and C can fill a tank together in 8 hours. After working at it together for 2 hours, B is closed and A and C can fill the remaining part in 9 hours. The time in which B alone can fill the tank is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 24 hours
Together, A, B and C fill \( \frac{1}{8} \) of the tank per hour. In 2 hours they fill \( \frac{2}{8}=\frac{1}{4} \), so \( \frac{3}{4} \) is left.
A and C fill this \( \frac{3}{4} \) in 9 hours:
\( \displaystyle \text{A and C per hour}=\frac{3/4}{9}=\frac{1}{12} \)
B’s share of the joint rate is the difference:
\( \displaystyle \text{B per hour}=\frac{1}{8}-\frac{1}{12} \)
\( \displaystyle =\frac{3-2}{24}=\frac{1}{24} \)
So B alone fills the tank in 24 hours.