Two pipes A and B can fill a tank in 10 hours and 15 hours respectively. If both pipes are opened together in the empty tank, how long will they take to fill it?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6 hours
In one hour, A fills \(\frac{1}{10}\) of the tank and B fills \(\frac{1}{15}\) of the tank. Working together, the parts filled per hour add up:
\( \displaystyle \frac{1}{10} + \frac{1}{15} = \frac{3 + 2}{30} \)
\( \displaystyle = \frac{1}{6} \)
So together they fill the tank in 6 hours.
Why the other options are incorrect
Option (2) 8 hours — Incorrect. In 8 hours the two pipes would fill \(\frac{8}{6}\) of the tank, more than the whole tank.
Option (3) 12.5 hours — Incorrect. This is the average of 10 and 15 hours. Two pipes together must take less time than the faster pipe alone.
Option (4) 25 hours — Incorrect. This adds the two times; the times do not add, the parts filled per hour do.