Question : Two pipes can independently fill a bucket in 20 minutes and 25 minutes. Both are opened together for 5 minutes after which the second pipe is turned off. What is the time taken by the first pipe alone to fill the remaining portion of the bucket?
Option 1: 11 minutes
Option 2: 16 minutes
Option 3: 20 minutes
Option 4: 15 minutes
Correct Answer: 11 minutes
Solution :
1 minute work of first pipe = $\frac{1}{20}$
1 minute work of second pipe = $\frac{1}{25}$
After 5 minutes of operation, the fraction of the work completed
= ($\frac{1}{20}$ + $\frac{1}{25}$) × 5
= $\frac{9}{100}$ × 5
= $\frac{9}{20}$
Remaining part $=(1-\frac{9}{20})=\frac{11}{20}$
The remaining tank will be filled by the first pipe alone with an efficiency of $\frac{1}{20}$,
that is in ($\frac{11}{20}\div \frac {1}{20})= 11 $ minutes
Hence, the correct answer is 11 minutes.
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