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 2 of 7.
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)
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)
Rofiqul Hoque said:
1 decade ago
Let 1st pipe take time = x hours.
2nd pipe is 5 hours faster means its take 5 hours less than 1st pipe.
i.e., 2nd = (x-5) hours.
3rd pipe is 4 hours slower than the 2nd pipe.
i.e., 3rd +4 = (x-5).
=>3rd = (x-5) -4.
=>3rd = x-9.
Now,
1/x + 1/ (x-5) =1/ (x-9).
Dear friends now just solve it. Bye friends meet you again.
2nd pipe is 5 hours faster means its take 5 hours less than 1st pipe.
i.e., 2nd = (x-5) hours.
3rd pipe is 4 hours slower than the 2nd pipe.
i.e., 3rd +4 = (x-5).
=>3rd = (x-5) -4.
=>3rd = x-9.
Now,
1/x + 1/ (x-5) =1/ (x-9).
Dear friends now just solve it. Bye friends meet you again.
Kasi Srinivas said:
1 decade ago
@ sai :
first pipe alone takes x hours to fill the tank => in 1 hour 1/x part of the work is completed.
similar way we get 1/(x-5) and 1/(x-9) part of the work is completed in 1 hour.
it is the standard practice that we consider the work done in an hour.
If you understood the question properly, you can understand this :)
first pipe alone takes x hours to fill the tank => in 1 hour 1/x part of the work is completed.
similar way we get 1/(x-5) and 1/(x-9) part of the work is completed in 1 hour.
it is the standard practice that we consider the work done in an hour.
If you understood the question properly, you can understand this :)
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)
Bhagyasree said:
8 years ago
Suppose A takes x hours then B takes x-5 hours.
Ex: It means that A completed in 10 hours where B Completed only in 5 hours
Now C take y hours where B Completes in y+4 hours(slower),
So x-5 =y+4..............y=x-9,
Here capability of A+B = C,
1/x+1/x-5 = 1/y,
Now, You can easily solve this eq 1/x+1/x-5 = 1/x-9.
Ex: It means that A completed in 10 hours where B Completed only in 5 hours
Now C take y hours where B Completes in y+4 hours(slower),
So x-5 =y+4..............y=x-9,
Here capability of A+B = C,
1/x+1/x-5 = 1/y,
Now, You can easily solve this eq 1/x+1/x-5 = 1/x-9.
Deepi said:
1 decade ago
@ venky
See the question they have given as second pipe 5 hours faster than the first and 4 hours slower than third.
Lets consider first pipe takes X hrs for ex. 10hrs
Second pipe takes 5 hours faster than first it means 5hrs (X-5)
Third pipe is faster than second by 4hrs. That is 1hour(10-9)=(X-9).
See the question they have given as second pipe 5 hours faster than the first and 4 hours slower than third.
Lets consider first pipe takes X hrs for ex. 10hrs
Second pipe takes 5 hours faster than first it means 5hrs (X-5)
Third pipe is faster than second by 4hrs. That is 1hour(10-9)=(X-9).
Brryne said:
9 years ago
Dear Friends. The solution according to me is correct.
The reason as to why X = 3 is neglected is because there is no negative time.
For example: 3 hrs. If you substitute X with 3, then,
1/(x-5) will be 1/(3-5).
Which are 1/-2 hours (negative thirty minutes: never in real life!)
The reason as to why X = 3 is neglected is because there is no negative time.
For example: 3 hrs. If you substitute X with 3, then,
1/(x-5) will be 1/(3-5).
Which are 1/-2 hours (negative thirty minutes: never in real life!)
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)
Santosh h said:
9 years ago
Just remember these:
1. Faster fil = lesser time.
2. If total time=x, then for 1 hr it is 1/x.
3. When you get two different answers after solving the equation just substitute the answers (like x=15) in the original equation and check whether it is feasible.
1. Faster fil = lesser time.
2. If total time=x, then for 1 hr it is 1/x.
3. When you get two different answers after solving the equation just substitute the answers (like x=15) in the original equation and check whether it is feasible.
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