Two taps A and B can fill a tank in 10 hours and 15 hours respectively. If both taps are opened together, the tank will be full in:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 6 hours
When two taps work together, the parts of the tank they fill in one hour add up; the time for the whole tank is the reciprocal of that sum.
Tap A fills \(\frac{1}{10}\) of the tank in an hour, and tap B fills \(\frac{1}{15}\)
Together in one hour: \(\displaystyle\frac{1}{10}+\frac{1}{15}=\frac{3+2}{30}=\frac{1}{6}\) of the tank
The whole tank therefore takes 6 hours
Shortcut:
For two taps, time together \(=\displaystyle\frac{\text{product of the times}}{\text{sum of the times}}=\frac{10\times15}{10+15}=\frac{150}{25}=6\) hours