A tank can be filled by one tap in 20 minutes and by another tap in 60 minutes. Starting with the tank empty, both taps are kept open for 10 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) → 20 minutes
While both taps run, their one-minute parts add up; the part still empty after 10 minutes is filled by the second tap alone.
Both taps in one minute \(\displaystyle =\frac{1}{20}+\frac{1}{60}=\frac{3+1}{60}=\frac{1}{15}\) of the tank
Filled in 10 minutes \(\displaystyle =10\times\frac{1}{15}=\frac{2}{3}\)
Part left \(\displaystyle =1-\frac{2}{3}=\frac{1}{3}\)
Second tap fills \(\frac{1}{3}\) of the tank in \(\displaystyle \frac{1}{3}\times60=20\) minutes
The tank is full 20 minutes after the first tap is shut off (30 minutes after the start).