31.  2 pipes A & B can fill a tank in 15 hrs and 20 hrs respectively while a 3'rd pipe C can empty the full tank in 25 hrs. All the 3 pipes are opened in the beginning. After 10 hrs C is closed. In how much time will the tank be full?

12 hrs
13 hrs
16 hrs
18 hrs

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Answer: Option  A Explanation:Part filled in 10 hrs= 10 ( 1/15 + 1/20 - 1/25 ) = 23/30
Remaining part = (1-23/30) = 7/30
(A+B)'s 1 hrs work = (1/15 + 1/20) = 7/60
x= (7/30 * 1* 60/7) = 2 hrs
Hence the tank will be full in (10+2) hrs = 12 hrs. ```

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32.  2 pipes A & B can fill a tank in 15 minutes and 20 minutes respectively.Both the pipes are opened together but after 4 minutes pipe A is turned off.What is the total time required to fill the tank?

10 mins 20 sec
11 mins 45 sec
12 mins 30 sec
14 mins 40 sec

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Answer: Option  D Explanation:Part filled in 4 mins = 4(1/15 + 1/20) = 7/15
Remaining part = ( 1-7/15) = 8/15
Part filled by B in 1 minute = 1/20
X = (8/15*1*20) = 10 2/3 min.=10 min 40 sec.
The tank will be full in( 4 min + 10 min 40 sec) = 14 min.40 sec. ```

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33.  Two pipes A & B can fill a tank in 12 mins and 15 mins respectively.If both the taps are opened simultaneously and the tap A is closed after 3 minutes than how much more time will it take to fill the tank by tap B?

7 mins 15 sec
7 mins 45 sec
8 min 5 sec
8 min 15 sec

```Answer

Answer: Option  D Explanation:Part filled in 3 mins = 3 (1/12 + 1/15) = (3*9/16) = 9/20.
Remaining part = (1-9/20) = 11/20
Part filled by B in 1 minute = 1/15
x= (11/20 * 1* 15) = 8 1/4 minute = 8 min 15 sec
Remaining part is filled by B in 8 mins 15 sec ```

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34.  A tank is filled by 3 pipes with uniform flow.The first 2 pipes operating simultaneously fill the tank in the same time during which the tank is filled by the 3'rd pipe alone.The 2'nd pipe fills the tank 5 hrs faster than the 1'st pipe and 4 hrs slower than the 3'rd pipe.The time required by the first pipe is?

6 hrs
10 hrs
15 HRS
30 HRS

```Answer

Answer: Option  C Explanation:SUPPOSE 1'st pipe alone takes x hrs.To fill the tank than 2'nd & 3'rd pipes will take (x-5) & ( x-9) hrs respectively to fill the tank.
therefore 1/x+1/(x-5) = 1/(x-9) = x-5 +x / x(x-5) = 1/(x-9)
(2x-5) (x-9) =x(x-5) = x (x-5) = x^2 -18x +45 =0
(x-15) (x-3) = 0 =
x=15 ```

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35.  A tank is filled in 5 hours by three pipes A,B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank ?

20 hrs
25 hrs
35 hrs
None of these

```Answer

Answer: Option  C Explanation:Suppose pipe A alone takes  x hrs to fill the tank then
Pipes B and C will take x/2 and x/4 hrs respectively to fill the tank
1/x+2/x+4/x = 1/5 = 7/x = 1/5 = 35 hrs ```

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