Question : Each inlet pipe can fill an empty cistern in 84 hours while each drain pipe can empty the same cistern from a filled condition in 105 hours. When the cistern is empty, 9 inlet pipes and 10 outlet pipes are simultaneously opened. After how many hours will the cistern be filled?
Option 1: 84
Option 2: 88
Option 3: 80
Option 4: 90
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Correct Answer: 84
Solution :
Time taken by inlet pipe = 84 hours
Time taken by outlet pipe = 105 hours
LCM of 84 and 105 (total work to be done) = 420 units
$\therefore$ Efficiency of inlet pipe = $\frac{420}{84}$ = 5 Units
Efficiency of outlet pipe = $\frac{420}{105}$ = 4 Units
Efficiency of $9$ inlet pipes = $9×5=45$ Units
Efficiency of $10$ outlet pipes = $10×4=40$ Units
$\therefore$ Effective filling efficiency = $45-40=5$ Units
So, time taken = $\frac{420}{5}=84 $ hours
Hence, the correct answer is 84.
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