Two pipes A and B can fill a tank in 9 hours and 12 hours respectively. Both pipes are opened together in the empty tank. What part of the tank will be filled in 3 hours?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{7}{12}\)
In one hour each pipe fills the reciprocal of its time, and the parts filled together are added.
\(\displaystyle \text{Part filled in 1 hour} = \frac{1}{9} + \frac{1}{12} = \frac{4 + 3}{36} = \frac{7}{36}\)
\(\displaystyle \text{Part filled in 3 hours} = 3 \times \frac{7}{36} = \frac{7}{12}\)
So \(\displaystyle\frac{7}{12}\) of the tank is filled in 3 hours.