Two pipes A and B can fill an empty tank in 10 hours and 16 hours respectively. They are opened alternately for 1 hour each, pipe B being opened first. In how many hours will the empty tank be filled?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(12\frac{2}{5}\)
Take the tank as the LCM of 10 and 16, that is 80 units. Each 2-hour round (B, then A) adds a fixed amount; the last part is filled by whichever pipe is due next.
A fills \(\frac{80}{10}=8\) units per hour, B fills \(\frac{80}{16}=5\) units per hour
One round of 2 hours \(=5+8=13\) units
6 rounds \(=12\) hours, filling \(6\times13=78\) units
Units left \(=80-78=2\); the 13th hour is B's turn
B fills 2 units in \(\frac{2}{5}\) hour
The tank is full in \(12\frac{2}{5}\) hours.