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# Aptitude - Pipes and Cistern - Discussion

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"Loneliness is the most terrible poverty."
- Mother Teresa
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:

 [A]. 6 hours [B]. 10 hours [C]. 15 hours [D]. 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]

 Prasad said: (Fri, Dec 31, 2010 01:57:00 AM) How you have taken 9 hours?

 Vijay said: (Wed, Jan 12, 2011 11:14:12 PM) As 2nd one is 4 hrs slower than 3rd pipe, 3rd pipe should be 4 hrs faster than 2nd. So, 3rd pipe is 9 hrs faster than 1st one.

 Pranesh Kumar said: (Sun, May 29, 2011 11:51:50 PM) Why you neglect x=3 for what reasons?

 Karthikeyan said: (Thu, Jun 2, 2011 06:22:14 AM) How got this equation 1/x+1/x-5=1/x-9 ?

 Manasa said: (Sat, Jun 11, 2011 09:00:33 AM) @pranesh kumar In options "3" is not given...so we considered 15 both "3" and "15" are correct. @karthikeyan In the question they given The first two pipes operating simultaneously fill the tank(1/x+1/X-5)... in the same time means ("=") during which the tank is filled by the third pipe alone(1/X-9) how much water gets filled up by the first two pipes in 1 hour...the same amount of water gets filled up by the third pipe in 1 hour.

 Sachin said: (Sat, Aug 6, 2011 02:13:25 AM) How can a pipe fill in both 3 and 9 hours. Hows it possible? Only one answer must be true? which one how to get?

 Praneeth said: (Sat, Aug 6, 2011 05:15:13 PM) 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.

 Sai said: (Wed, Aug 31, 2011 06:39:18 PM) Why we have taken 1/x, 1/x-5, 1/x-9. Please can any one say me the reason?

 Kasi Srinivas said: (Thu, Sep 1, 2011 12:18:43 PM) @ 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 :)

 Ghousia said: (Tue, Sep 6, 2011 11:17:53 PM) 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.

 Sai Krishna A said: (Thu, Nov 10, 2011 10:17:19 PM) @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

 Venky said: (Tue, Jan 17, 2012 08:53:47 PM) 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}

 Deepi said: (Mon, Feb 6, 2012 12:40:29 PM) @ 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).

 Rofiqul Hoque said: (Wed, Jun 27, 2012 11:03:16 AM) 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.

 Chinna Jgc said: (Wed, Aug 22, 2012 12:17:39 AM) 2nd pipe is 5 hours faster than 1st.so 2nd pipe=5x 1st pipe automatically takes 1 hour to fill the tank.1st pipe=1x. in question 2nd pipe is 4 hours slower than 3rd pipe. i.e 5x+4x=9x 3rd pipe =9x add all 3 pipes i.e 1x+5x+9x=15.