Question : Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes, P is turned off. In how many more minutes will Q fill the cistern?
Option 1: $7$ minutes
Option 2: $7\frac{1}{2}$ minutes
Option 3: $8$ minutes
Option 4: $8\frac{1}{4}$minutes
Correct Answer: $8\frac{1}{4}$minutes
Solution :
P can fill a cistern in 12 minutes and Q in 15 minutes.
LCM of 12 and 15 is 60.
Let the total work be 60 units.
The efficiency of P per minutes is $\frac{60}{12}$ = 5 units and Q is $\frac{60}{15}$ = 4 units
In 3 minutes together they can fill = 3 × (5 + 4) = 27 units
The remaining = 60 – 27 = 33 units
Now that P is closed, the remaining water will be filled by Q with the efficiency of 4 units per minute
$=\frac{33}{4} =8\frac{1}{4}$ minutes
Hence, the correct answer is $8\frac{1}{4}$ minutes.
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