Aptitude - Pipes and Cistern - Discussion
Discussion Forum : Pipes and Cistern - General Questions (Q.No. 3)
3.
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2
hours to fill the tank. The leak can drain all the water of the tank in:
hours to fill the tank. The leak can drain all the water of the tank in:Answer: Option
Explanation:
| Work done by the leak in 1 hour = |  |
1 | - | 3 |  |
= | 1 | . |
| 2 | 7 | 14 |
Leak will empty the tank in 14 hrs.
Discussion:
90 comments Page 2 of 9.
Yamini Dhanasekar said:
7 years ago
It can also solved by;
Let the Filling pump be 'A' and leakage be 'B'.
A takes 2 hrs to fill, In 1 hr -it will complete 1/2 of the work, ie half of the tank.
In addition of B,
A-B=2 1/3 hrs, In 1 hr they complete 1/21/3 which is;
A-B=3/7.
We can substitute A,
1/2 -B=3/7
B=1/14.
So, In hr, B drains 1/14 part of the tank.
Total work-1.
Hr -- work
1 -- 1/14
? -- 1.
1/1/14= 14 hours.
Let the Filling pump be 'A' and leakage be 'B'.
A takes 2 hrs to fill, In 1 hr -it will complete 1/2 of the work, ie half of the tank.
In addition of B,
A-B=2 1/3 hrs, In 1 hr they complete 1/21/3 which is;
A-B=3/7.
We can substitute A,
1/2 -B=3/7
B=1/14.
So, In hr, B drains 1/14 part of the tank.
Total work-1.
Hr -- work
1 -- 1/14
? -- 1.
1/1/14= 14 hours.
Mr Pai said:
5 years ago
Time taken by the pump to fill the tank = 2 hours
Work done by the pump in 1 hour = 1/2
Time taken by the pump to fill with leakage = 7/3
Work done by the pump with leakage in 1 hour = 3/7
Time taken by the leakage to empty the tank = x hours
Work done by the leakage in 1 hour = 1/x.
Therefore, (1/2)-(1/x) = 3/7.
-1/x = (3/7)-(1/2).
-1/x = (6-7)/14.
x = 14 hours.
Work done by the pump in 1 hour = 1/2
Time taken by the pump to fill with leakage = 7/3
Work done by the pump with leakage in 1 hour = 3/7
Time taken by the leakage to empty the tank = x hours
Work done by the leakage in 1 hour = 1/x.
Therefore, (1/2)-(1/x) = 3/7.
-1/x = (3/7)-(1/2).
-1/x = (6-7)/14.
x = 14 hours.
(1)
Behara Satish Kumar said:
6 years ago
Let v take two pipes A&B,
Let time of A=2hrs = 120months
Therefore the capacity of A(per mnt) = 1/120.
Now,
The time is taken by B=2 1/3 hrs = 140months.
Therefore the capacity of B(per mnt) = 1/140.
The difference between two pipes be the leakage capacity
i.e A-B = (1/120)-(1/140) = 1/840.
Therefore time was taken of leak = 840mnts = 14h.
Let time of A=2hrs = 120months
Therefore the capacity of A(per mnt) = 1/120.
Now,
The time is taken by B=2 1/3 hrs = 140months.
Therefore the capacity of B(per mnt) = 1/140.
The difference between two pipes be the leakage capacity
i.e A-B = (1/120)-(1/140) = 1/840.
Therefore time was taken of leak = 840mnts = 14h.
Suresh said:
4 years ago
Convert Hours into minutes.
A can fill in 2hrs i.e 120mins.
Leakage i.e a-b 2 1/3 is equal to 140mins.
Then capacity (LCM) is 840.
Efficiency : A is 7 and a-b is 6 and the difference is 1.
It can empty one part per minute out of 840 minutes. Then 840 parts can be emptied in 840 minutes.
Now convert 840 minutes to hours.
840/60 is 14 hours.
A can fill in 2hrs i.e 120mins.
Leakage i.e a-b 2 1/3 is equal to 140mins.
Then capacity (LCM) is 840.
Efficiency : A is 7 and a-b is 6 and the difference is 1.
It can empty one part per minute out of 840 minutes. Then 840 parts can be emptied in 840 minutes.
Now convert 840 minutes to hours.
840/60 is 14 hours.
(19)
DILIP KUMAR B K said:
3 years ago
As we know that rate (r)=work(w)/time(t).
Here the main thing is the work will remain constant.
Therefore,
As we have to find the time taken to empty the tank that is (T) with the leak will be;
W/T = (W/2 - W/(7/3)).
Cancelling "w" on both sides.
1/T = (1/2 - 3/7) = 1/14.
To get T,
We reciprocate the above result which is T = 14 hrs.
Here the main thing is the work will remain constant.
Therefore,
As we have to find the time taken to empty the tank that is (T) with the leak will be;
W/T = (W/2 - W/(7/3)).
Cancelling "w" on both sides.
1/T = (1/2 - 3/7) = 1/14.
To get T,
We reciprocate the above result which is T = 14 hrs.
(11)
Pranav said:
8 years ago
Ans : D
Tank fill without leak = 2 hours
Tank fill with leak = 2 1/3 hours
= 2/1 * 1/3
= 7/3 hours
(imp)
The time taken to drain a tank is
= Part filled in 1 hour (without leak) - partly filled in 1 hour (with leak).
= 1/2 - 1/ 7/3
=> 1/ 7/3 = 3/7
= 1/2 - 3/7
= 1/14.
So, time taken to drain the tank is 14 hours.
Tank fill without leak = 2 hours
Tank fill with leak = 2 1/3 hours
= 2/1 * 1/3
= 7/3 hours
(imp)
The time taken to drain a tank is
= Part filled in 1 hour (without leak) - partly filled in 1 hour (with leak).
= 1/2 - 1/ 7/3
=> 1/ 7/3 = 3/7
= 1/2 - 3/7
= 1/14.
So, time taken to drain the tank is 14 hours.
Mrunal said:
8 years ago
Here is a different solution.
Let tank capacity is 42 liters.
Pump A filling rate is = 42 liters/ 2 hours= 21 lph.
Pump A filling rate due to the leak is = 42 liters/ 7/3 hours = 18 lph.
Now the leaking rate is 21-18= 3 lph.
Leak can empty tank in = 42 liters/ 3 lph= 14 hrs.
Hope this is simple and easy to understand.
Let tank capacity is 42 liters.
Pump A filling rate is = 42 liters/ 2 hours= 21 lph.
Pump A filling rate due to the leak is = 42 liters/ 7/3 hours = 18 lph.
Now the leaking rate is 21-18= 3 lph.
Leak can empty tank in = 42 liters/ 3 lph= 14 hrs.
Hope this is simple and easy to understand.
Mohanapriya said:
1 decade ago
2 hrs compose 120 mins.
But due to leak it takes 120+20 = 140 mins.
1st 2hr - 20 goes of [the amount has to be filled in 20 mins].
4nd hr - 40 mins.
6th hr - 60 mins.
8th hr - 80 mins.
10th hr - 100 mins.
12th hr - 120 mins.
14th hr - 140 mins.
And so it takes 14 hours to empty a full tank.
But due to leak it takes 120+20 = 140 mins.
1st 2hr - 20 goes of [the amount has to be filled in 20 mins].
4nd hr - 40 mins.
6th hr - 60 mins.
8th hr - 80 mins.
10th hr - 100 mins.
12th hr - 120 mins.
14th hr - 140 mins.
And so it takes 14 hours to empty a full tank.
Siddu said:
6 years ago
A initially fills in 2 hrs.
Hence in one hr it fills 1/2 units,
With leak it takes 7/3 hrs,
Hence in one hr it fills 3/7 units (with leak).
(1/2)- leak per unit = 3/7,
Leak per unit = (1/2)-(3/7),
=1/14.
Per hr, it leaks units 1/14.
Total time taken to empty is 14 hrs.
Hence in one hr it fills 1/2 units,
With leak it takes 7/3 hrs,
Hence in one hr it fills 3/7 units (with leak).
(1/2)- leak per unit = 3/7,
Leak per unit = (1/2)-(3/7),
=1/14.
Per hr, it leaks units 1/14.
Total time taken to empty is 14 hrs.
Dhivyanisan said:
4 years ago
Time is taken by pump without leak = 2hrs.
Its discharge capacity says a= 1/2.
Time is taken by a pump with leak = 2 (1/3)hrs or 7/3 hrs.
It's discharge capacity say b= 1/(7/3) = 3/7.
So discharge capacity of the leak is a-b = 1/14.
Time taken by the leak to empty tank = 1/(1/14) = 14 hrs.
Its discharge capacity says a= 1/2.
Time is taken by a pump with leak = 2 (1/3)hrs or 7/3 hrs.
It's discharge capacity say b= 1/(7/3) = 3/7.
So discharge capacity of the leak is a-b = 1/14.
Time taken by the leak to empty tank = 1/(1/14) = 14 hrs.
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