# Aptitude - Pipes and Cistern - Discussion

Discussion Forum : Pipes and Cistern - General Questions (Q.No. 5)
5.
A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:
6 hours
10 hours
15 hours
30 hours
Explanation:

Suppose, first pipe alone takes x hours to fill the tank .

Then, second and third pipes will take (x -5) and (x - 9) hours respectively to fill the tank.

 1 + 1 = 1 x (x - 5) (x - 9)

 x - 5 + x = 1 x(x - 5) (x - 9)

(2x - 5)(x - 9) = x(x - 5)

x2 - 18x + 45 = 0

(x - 15)(x - 3) = 0

x = 15.    [neglecting x = 3]

Discussion:
67 comments Page 1 of 7.

DEVINDER SINGH said:   6 months ago
Why equating work of a+b = work of c.

till the time we used the method
a = x-5
b = x
c =x-4.
Acc to the question.
(x-5) + x = x-4 on solving;
a = 4.
b = 9.
c = 13 which seems feasible acc conditions and also we used earlier questions.
(3)

Yogi said:   1 year ago
Thanks a lot for your explanation @Nita.
(3)

Hitesh said:   2 years ago

3 and 15 but for 3 we will get y= -2 from y+5 =x,

So, x = 15.
(3)

Anonymous said:   3 years ago
Thanks @Sai Krishna.

SHUBHADIP DAS said:   3 years ago
In how much time 2nd and 3rd pipe together fo the work? Please explain the answer.
(1)

Sarbajit rai said:   4 years ago
@Ghousia,

Here the question says to find the time and thus it is logical that lesser the time it takes faster will be the work in filling the tank. For instance, car A is moving faster than car B by 10 kmph means car A is taking less time to cover the same as that of car B. That is the reason why 1/x+1/ (x-5) =1/(x-9).
(3)

Amaterasu said:   4 years ago
Consider 1st, 2nd and 3rd pipe as a,b,c.

Given 1/a+1/b=1/c or a+b/ab=1/c because the time taken to fill by a and b is same is c
b=a-5 can be written as a=b+5.
b=c+4.
1st put value of a in a+b/ab=1/c then u get 2b+5/(b+5)b = 1/c
Then put the value of b you will get c=6 so b will 10 and a will be 15.
And the time taken by a is 15hr.
(14)

Saimanasa said:   4 years ago
Thank you @Manasa.
(1)

Harshvardhan said:   5 years ago
Simple if we take X time taken by pipe 2 then,

Time is taken by first pipe 1 = X+5.
Time is taken by second pipe 2 = X.
Time is taken by third pipe 3 = X-4.
So as per the question,
Pipe 1 +pipe 2 = pipe 3.
1/(X+5) + X = 1/(X-4).
After solving this equation we will get X=10.

Then, we know that time taken by pipe 1 = X+5.
Simply put the X=10, so pipe 1 will take =15 hours.
(27)

Trinesh said:   5 years ago
Why it take x-5?

The second pipe fills the tank 5 hours faster than the first pipe so there will be X+5.
(3)