Aptitude - Pipes and Cistern - Discussion

How to substitute this on for answer 1/2-3/7 =1/14?

Good explanation, Thank you @Mohanapriya.

@Mouni.
Work done for 1 hr without leak = 1/2,
Time taken to fill the tank with leak = 2 1/3hrs = 7/3 hrs,
Work done with leak in 1 hr = 3/7,
Work done by leak in 1 hr = 1/2 - 3/7 = 1/14,
So, tank will be empty by the leak in 14 hrs.

Here it is mentioned as 2 hrs for the tank and for leak tank time also given 2 hrs instead of 2hrs 20 min. SO I am also confused that how 3/7 comes?

Let A take 2hrs to fill.

B take 'x' hrs to empty the tank.
(A-B) per = 2 1/3hrs =7/3.
(A-B) per= Aper -Bper.
1/ (3/7) =1/2 - 1/x.
1/x = 1/2 - 7/3.
x = 14.

First, let's find the rate of filling up with and without leakage.

Assume that the volume of the tank is 2 liters (for easy calculation).
Then the rate of filling without leak = 1 liter/hour.
Rate of filling with leakage = 2 liters/ (7/3) hours = 6/7 liters per hour.
Now we get the leakage rate ie = 1 - 6/7 = 1/7 liters/hour.

So, time taken = total volume/rate of leakage = 2/ (1/7) = 14 hours.

@Paushali Mukhtoy is very well explained. Thank you.

For inlet it takes one hour for 1/2 part. For leakage, let's consider it takes 1 hour for 1/x parts.

For 2 hours and 20 minutes the tank will be filled as question says: (1/2-1/X)*7/3 = 1 (the full tank having 1 part).

@Mouni.

Please check this one:

Let us take Cistern is filled by pipe A and leak is due to pipe B (In this way it is easy to understand).

First point : Cistern filled by pipe A in 8 hrs.

Second point : Cistern filled by pipe A and pipe B (it is actually leak) is 10hrs (8+2).

Now take LCM of these two LCM of 8, 10 is 40. This implies to fill Cistern, total 40 units of work needed.

Then if only pipe A can fill the Cistern in 8 hrs that means 5 units of work for min by pipe A. Both pipe A and pipe B can fill the Cistern in 10 hrs that means 4 units of work by pipe A and pipe B.

So if you see, in second case 4 units of work per min where as in first case it is 5 units of work. This means if you include leak it reduces the work units by 1 unit ---> leakage per hr is 1 unit.

So to drain all the water in cistern, leak has to do 40 units of work. So if it is doing 1 unit of work to drain the tank. For 40 units it has to 40 hrs of work. So answer : 40 hrs.

A cistern is normally filled in 8 hrs. But takes 2 hrs more to fill because of a leak in its bottom. If the cistern is full, the tank will empty it in?

Please tell me with explanation.