Quant Quiz - (Pipes & Cistern )

Q1)-A pump can fill a tank with water in 2 hours. Because of a leak, it took 2(1/3) hours to fill the tank. The leak can drain all the water of the tank in:

4 hours

7 hours

8 hours

14 hours

Ans.- D
Work done by the leak in 1 hour = ( 1/2 - 3/7 ) = 1/14
Leak will empty the tank in 14 hours

Q2)-Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long it will take to fill the tank ?

10 mins

12 mins

14 mins

15 mins

Ans.- B
Part filled by A in 1 min = 1/20
Part filled by B in 1 min = 1/30
Part filled by (A+B) in 1 min = 1/20 + 1/30= 1/12
So both pipes can fill the tank in 12 mins.

Q3)-A pump can fill a tank with water in 2 hours. Because of a leak, it took 2(2/3) hours to fill the tank. The leak can drain all the water of the tank in

6 hours

8 hours

9 hours

10 hours

Ans.- B
The pump can fill the tank in 2 hour. But, because of the leak, it took 2(2/3) hours to fill the tank.
i.e., the additional water filled by the pump in 2/3 hour is emptied by the leak in 2(2/3)=8/3 hours.
Therefore, the water filled by pump in 2 bour can be emptied by the leak in (8/3)×3=8 hours.
i.e., The leak can drain all the water of the tank in 8 hours.

Q4)-A cistern can be filled by a tap in 12 hours and by the other tap in 9 hours. If both taps are opened together how long will it take to fill the cistern?

37/7 hours

36/7 hours

35/4 hours

None of these

Ans.- B
Time taken by the 1st tap to fill the cistern = 12 hours
Therefore, work done by the 1 st tap in 1 hour = 1/12
Time taken by the 2nd tap to fill the cistern = 9 hours.
Therefore, work done by the 2nd tap in 1 hour = 1/9
Therefore, work done by the both taps in 1 hour = 1/12 + 1/9
= (3 + 4)/36
= 7/36
Therefore, both taps will fill the cistern in = 36/7 hours.

Q5)-A tank can be filled by two tap A and B in 8 hour and 10 hours respectively. The full tank can be emptied by the third tap in 9 hours. If all the taps be turned on at the same time, in how much time will the empty tank be filled up completely?

3601/6 hours

360/41 hours

45/4 hours

None of these

Ans.- B
Time taken by tap A to fill the tank = 8 hours
Time taken by tap B to fill the tank = 10 hours
Time taken by tap C to fill the tank = 9 hours
Therefore, tap A fills 1/8 th part of the tank in 1 hour.
Tap B fills 1/10 th part of the tank in 1 hour.
Tap C empties out 1/9 th part of the tank in 1 hour.
Thus, in 1 hour (1/8 + 1/10 – 1/9) part of the tank is filled.
(45 + 36 – 40)/360 = 41/360 th part of the tank is filled.
Thus, tank will be filled completely in 360/41 hours, when all the three taps A, B and C are opened together.

Q6)-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 the first is turned off. How much longer will the cistern take to fill?

9 1/4 min

11 1/4 min

7 1/4 min

8 1/2 min

Ans.- B
3/12 + x/15 = 1
x= 11 1/4

Q7)-A pipe can fill the tank in 5 hours. Due to leakage at the bottom it is filled in 6 hours. When the tank is full, in how much time will it be empties by the leak?

10 hours

20 hours

30 hours

40 hours

Ans.- C
When there is no leakage, the pipe can fill the cistern in 5 hours.
Therefore, The pipe fills 1/5 th part of the tank in one hour.
When there is a leakage, the pipe can fill the cistern in 6 hours.
In case of leakage, the pipe fills 1/6 th part of the tank in one hour.
So, in 1 hour due to leakage (1/5 – 1/6) th= (6 – 5)/30 th
= 1/30 th
The part of the tank is emptied.
So, the tank will be emptied by leakage in 30 hours.

Q8)-A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

3 hrs 15 min

3 hrs 45 min

4 hrs 15 min

None of these

Ans.- B
Time taken by one tap to fill half of the tank = 3 hours
Part filled by the four taps in 1 hour = ( 4 x 1/6) = 2/3
Remaining part = (1 - 1/2) = 1/2
2/3 : 1/2 :: 1 : x
x = ( 1/2 x 1 x 3/2) = 3/4
So total time taken = 3 hours 45 mins

Q9)-Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?

7 min

13 min

23 min

9 min

Ans.- D
1/10 + 1/15 - 1/x = 1/18
x = 9

Q10)-A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills water at the rate of 6 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many liters does the cistern hold?

7580

7980

8640

8290

Ans.- C
Work done by the inlet in 1 hour = 1/8 - 1/12 = 1/24
Work done by the inlet in 1 min. = 1/24 * 1/60 = 1/1440
Given, volume of 1/1440 part = 6 liters.
Volume of whole = 6 * 1440 = 8640 liters.