A tank can be filled by one tap in 15 minutes and by another tap in 45 minutes. Starting with the tank empty, both taps are kept open for 6 minutes and then the first tap is shut off. In how much more time will the tank be completely filled?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 21 minutes
While both taps run, their one-minute parts add up; the part still empty after 6 minutes is filled by the second tap alone.
Both taps in one minute \(\displaystyle =\frac{1}{15}+\frac{1}{45}=\frac{3+1}{45}=\frac{4}{45}\) of the tank
Filled in 6 minutes \(\displaystyle =6\times\frac{4}{45}=\frac{24}{45}\)
Part left \(\displaystyle =1-\frac{24}{45}=\frac{21}{45}\)
Second tap fills \(\frac{21}{45}\) of the tank in \(\displaystyle \frac{21}{45}\times45=21\) minutes
The tank is full 21 minutes after the first tap is shut off (27 minutes after the start).