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  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 = 41-1= (4 / 12) = (1 / 3)
612

After 4 hr, P is closed and for 6 more hr Q and R are opened.
So part of tank filled = 61-1= (1 / 6)
912

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

63122

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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