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#### Numerical Ability

1. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed. The total time taken to fill the tank (in hours) is _____.
1. 13.50
2. 16.50
3. 14.50
4. 15.50
##### Correct Option: C

Here,

 In 1 hr, part of tank filled by P alone is = 1 6

 In 1 hr, part of tank filled by Q alone is = 1 9

 In 1 hr, part of tank emptied by R is = 1 12

Initially, P and R opened for 4 hr,
 So part of tank filled = 4 1 - 1 = (4 / 12) = (1 / 3) 6 12

After 4 hr, P is closed and for 6 more hr Q and R are opened.
 So part of tank filled = 6 1 - 1 = (1 / 6) 9 12

 So, total tank filled in 10 hr = 1 + 1 = 2 + 4 = 1 6 3 12 2

So, remaining 1/2 part of the tank is filled by Q alone
Now, Q will take 9/2 = 4.5 hr to fill remaining half of the tank.
Hence, total time taken = 4 + 6 + 4.5 = 14.5 hr

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