Pipe A can fill an empty tank in 15 hours and pipe B can fill it in 10 hours. The tank is empty at 7 a.m., when pipe A is opened. Pipe B is opened at 9 a.m., and both pipes then stay open. At what time will the tank be full?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2:12 p.m.
Take the capacity as the LCM of 15 and 10, that is 30 units. Pipe A works alone from 7 a.m. to 9 a.m., and both pipes work after that.
A fills \(\frac{30}{15}=2\) units and B fills \(\frac{30}{10}=3\) units in one hour
7 a.m. to 9 a.m. (A alone): \(2\times2=4\) units
Left \(=30-4=26\) units, filled at \(2+3=5\) units per hour
Time \(\displaystyle =\frac{26}{5}=5\frac{1}{5}\) hours \(=5\) hours \(12\) minutes
9 a.m. \(+\;5\) hours \(12\) minutes \(=2{:}12\) p.m.
The tank is full at 2:12 p.m.