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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