Question : A water tank can be filled by a tap in 30 minutes and another tap can fill it in 60 minutes. If both the taps are kept open for 5 minutes and then the first tap is closed, how long will it take for the remaining tank to be full?
Option 1: 20 minutes
Option 2: 25 minutes
Option 3: 30 minutes
Option 4: 45 minutes
Correct Answer: 45 minutes
Solution : One minute's work of Tap A = $\frac{1}{30}$ One minute's work of Tap B = $\frac{1}{60}$ For 5 minutes, both taps are open $(\frac{1}{30}+\frac{1}{60})$×5 = $\frac{15}{60}$ = $\frac{1}{4}$ part of tank is full in 5 minutes Remaining part $=1-\frac{1}{4}=\frac{3}{4}$ So, $\frac{3}{4}$ of the remaining is to be filled by Tap B. The required time $=\frac{ \frac{3}{4}}{\frac{1}{60}} = \frac{3}{4}\times 60 =45$ minutes Hence, the correct answer is 45 minutes.
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