A tap can fill a tank in 45 minutes whereas another tap can empty it in 1 hour 30 minutes. If both taps are opened at 9 A.M., then the time at which the tank will be filled is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10:30 A.M.
Work in parts of the tank per minute. 1 hour 30 minutes = 90 minutes.
\( \displaystyle \text{Filling tap: }\frac{1}{45}\text{ per minute} \)
\( \displaystyle \text{Emptying tap: }\frac{1}{90}\text{ per minute} \)
The emptying tap works against the filling tap, so its rate is subtracted. The net rate with both open is
\( \displaystyle \frac{1}{45}-\frac{1}{90}=\frac{2-1}{90} \)
\( \displaystyle =\frac{1}{90}\text{ of the tank per minute} \)
So the tank fills in 90 minutes = 1 hour 30 minutes. Starting at 9 A.M., it is full at 10:30 A.M.