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:
Answer: Option
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:
68 comments Page 1 of 7.
Harshvardhan said:
6 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.
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.
(49)
Amaterasu said:
5 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.
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.
(16)
DEVINDER SINGH said:
2 years 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.
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.
(10)
Rabindra said:
8 years ago
The ratio of performance is A:B;C = 1:5:9 if we take lcm then we get the tank capacity i.e 45litre that means,
1+5+9=45,
15=45,
per hour litre=45/15=3 litre.
A can fill 3 lite per hour and B can 15 lit/hour, C can fill in 27 lit/hour,
so A will take time,
45/3=15 hour.
1+5+9=45,
15=45,
per hour litre=45/15=3 litre.
A can fill 3 lite per hour and B can 15 lit/hour, C can fill in 27 lit/hour,
so A will take time,
45/3=15 hour.
(7)
Rekha said:
1 year ago
Why it is 1 as a numerator? Please explain to me.
(4)
Yogi said:
3 years ago
Thanks a lot for your explanation @Nita.
(4)
Hitesh said:
3 years ago
Here we got 2 answers.
3 and 15 but for 3 we will get y= -2 from y+5 =x,
So, x = 15.
3 and 15 but for 3 we will get y= -2 from y+5 =x,
So, x = 15.
(4)
Trinesh said:
6 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.
The second pipe fills the tank 5 hours faster than the first pipe so there will be X+5.
(4)
Sarbajit rai said:
5 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).
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)
Nita said:
6 years ago
If we subject pipe 3 (P3) = x.
Then pipe 2 (P2) = x+4 (since P2 is 4 hours slower than P3 )
And Pipe 1 ( P1) = ( x+4)+5= x+9 (since P1 is 5 hours slower than P2; indirectly implied in the question).
So, the question becomes;
1/(x+9) + 1/ (x +4) = 1/ x.
Solving the equation we get x =+6,-6;
Taking x=+6.
Then pipe1 = (x +9) = 6+9=> 15.
Then pipe 2 (P2) = x+4 (since P2 is 4 hours slower than P3 )
And Pipe 1 ( P1) = ( x+4)+5= x+9 (since P1 is 5 hours slower than P2; indirectly implied in the question).
So, the question becomes;
1/(x+9) + 1/ (x +4) = 1/ x.
Solving the equation we get x =+6,-6;
Taking x=+6.
Then pipe1 = (x +9) = 6+9=> 15.
(3)
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