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 4 of 7.
Pankaj said:
7 years ago
A+B = C.
Now,
Let A pipe fill the tank in =X hr.
2nd pipe 5 hr slower than A,
B = (X-5) hr
3rd pipe 4 hr slower than B,
C= X- (5+4) hr = (X-9) hr.
LCM Of (A+B) is;
A= X
X(X-5) LCM.
B=X-5.
A's 1hr work= X(X-5)/X = X-5.
B's 1hr work= X(X-5)/(X-5) = X.
_______________________________
A+B. = 2X-5
_________________________________
A+B =C.
X(x-5)/2x-5 = x-9,
X^2-5x/2x-5 = x-9 cross multiple,
2x^2-5x-18x+45 = x^2-5x (5x cancel out),
2x^2-18x+45,x^2 = 0,
X^2-18x+45 = 0,
X^2-(15+3)x+45= 0,
X^2-15x-3x+45 = 0,
X(x-15) - 3(x-15) = 0,
(X-15) (x-3) = 0,
Ans= 15 hr.
Now,
Let A pipe fill the tank in =X hr.
2nd pipe 5 hr slower than A,
B = (X-5) hr
3rd pipe 4 hr slower than B,
C= X- (5+4) hr = (X-9) hr.
LCM Of (A+B) is;
A= X
X(X-5) LCM.
B=X-5.
A's 1hr work= X(X-5)/X = X-5.
B's 1hr work= X(X-5)/(X-5) = X.
_______________________________
A+B. = 2X-5
_________________________________
A+B =C.
X(x-5)/2x-5 = x-9,
X^2-5x/2x-5 = x-9 cross multiple,
2x^2-5x-18x+45 = x^2-5x (5x cancel out),
2x^2-18x+45,x^2 = 0,
X^2-18x+45 = 0,
X^2-(15+3)x+45= 0,
X^2-15x-3x+45 = 0,
X(x-15) - 3(x-15) = 0,
(X-15) (x-3) = 0,
Ans= 15 hr.
Swapnil said:
7 years ago
1/x + 1/ (x-5) = 1/(x-9).
Why 1/(x-9) equate with 1/x + 1/ (x-5)?
Why 1/(x-9) equate with 1/x + 1/ (x-5)?
Reshma said:
8 years ago
Nice explanation @Tanu.
Venky said:
1 decade ago
4 hours slower than the third pipe = means how we took 1/X-9 and that also like this 1/X +1/X-5= 1/X-9
third pipe speed we dont know ...the how {x-9}
third pipe speed we dont know ...the how {x-9}
Sai Krishna A said:
1 decade ago
@ghousia faster means in less time. if for example A takes 20hours then B takes(20-5=15)hours not 20+5=25hours. got it
Ghousia said:
1 decade ago
Why is x-9 and x-5 taken as the pipe speed is represented faster then it should be x+9 and x+5? Please clarify my doubt.
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 :)
Sai said:
1 decade ago
Why we have taken 1/x, 1/x-5, 1/x-9. Please can any one say me the reason?
Praneeth said:
1 decade ago
We have considered the x-5 and x-9 as time taken by 2nd and 3rd pipes, but after substituting x=3 we will get -2hr and -7hr respectively for the 2nd and third pipes.
So, we cant have negative values for time practically.
So, we cant have negative values for time practically.
Anonymous said:
4 years ago
Thanks @Sai Krishna.
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers