Aptitude - Pipes and Cistern - Discussion

@Lavanya.

Answer is 3 mins.

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

Then, first pipe and third pipe will take (x + 5) and (x - 4) hours respectively to fill the tank.

1/(x+5) + 1/x = 1/(x-4)
( x + x + 5 ) / ( x^2 + 5x ) = 1/(x-4)
Srossmultiply ( 2x + 5 ) * ( x - 4 ) = 1 * (x^2 + 5x )
Solve, you get
(x - 10)(x + 2) = 0
x = 10. [neglecting x = -2]
1st pipe = x + 5 = 15 hours.

Can't we pick the 'B' to be as x and do the same things since When I did I got four first just by generally calculating it?

Thanks @Sai Krishna.

@All.

We can solve by using a single condition.

Here which is efficiency of p1 +p2 =efficiency of p3--->CONDITION
To find individual efficiencies, the traditional x method = time consuming.
So opt for option verification;
On verifying option C, we meet our condition.

Option C says;
p1 takes time---------> 15 hours,
then p2 would be ---->10 hrs(15-5 as from Q 5 hours faster=earlier than p1 so subract),
p3 would be----------> 6hrs (10-4 as from question 4hrs earlier than p2).
Now, for the times of p1, p2, p3 (15,10,6) find the LCM.

LCM = >30.
Derive individual efficiencies from it(use allegation method as follows).
eff of p1=30/15 =>2.
eff of p2=30/10 =>3.
eff of p3=30/6 =>5.

From our condition
verify eff of p1+p2 =eff of p3.
2 + 3 = 5.
So, the assumption option C, 15 hours, would be correct.

Can anyone help me?

If suppose A and B are filling a tank started at same time.
A alone can fill it in 'a' minutes B alone can fill it in 'b' minutes.
So we are taking (1/a)+(1/b)=1 to find the time.

But when they are filling it simultaneously why are we taking same (1/x+1/x-5=1/x-9)?
I think after completion of a ,b is started it means we have to take a+b right? But not (1/a)+(1/b).

Can anyone help me?

If suppose A and B are filling a tank started at same time.
A alone can fill it in 'a' minutes B alone can fill it in 'b' minutes.
So we are taking (1/a)+(1/b)=1 to find the time.

But when they are filling it simultaneously why are we taking same (1/x+1/x-5=1/x-9)?
I think after completion of a ,b is started it means we have to take a+b right? But not (1/a)+(1/b).

Can anybody answer my question with correct explanation that why we have neglected x=3 and answered x=5. I know the explanation but I want to now that does anybody else knows it.

@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.

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.