Aptitude - Pipes and Cistern - Discussion

If we take faster one as x,
Then d slower one will become 3x,

Thus the work done by them is equal to 1/36.

Therefore,

1/x + 1/(3x) = 1/36.
(3x + x)/(3x * x) = 1/36.
4/3x = 1/36.
x = 48.

Thus the slower one will become 144, thats the solution for taking x and 3x as the time.

First pipe x.
Second pipe 3 times faster then it is 3x.

Together will fill it in 36 min.
1/x+1/3x=1/36.

Then we will get x=48 minutes and 3x= 144 minutes faster pipe is 48 minutes Which takes less time and slower pipe is 144 minutes which takes more time.

If we take x+x/3 instead of 1/x+3/x we cannot get answer because the method of solving will be more complicated.

I have another solution,

Suppose slower pipe is taking X min, then in that time faster pipe will fill 3 tanks.

Now both start filling tanks,then when slower pipe will finishing filling till that time faster also done with filling 3 tanks.

Total number of tanks filled is Slower= 1, and faster = 3, sum total is 4 tanks, NOw time taken for filling 1 tank is 36, Therefore time taken for filling 4 tanks is 36*4 = 144.

Therefore it indicates same time taken by slower pipe also to complete fill the tanks.

Why can't we take x+3x=36 and why we are taking 1/x+3/x=1/36 explain this solution in detail?

Why can't we take x+3x=36 and how 1/x+3/x is taken?

@Senthil.

Lets start afresh,

If you think in terms of speed/rate of filling the tank of 'l' Litres capacity, then the speed of slower pipe will be x litre/min and the speed of faster pipe will be 3x litre/min.

But, if you think in terms of time, then the slower pipe will take x min(or 3x min) and the faster one will take x/3 min(or x min) to fill the tank.

Now, if you consider the second case i.e.,consider in terms of time, then you will only need to find out how much portion of the tank's capacity each pipe can fill in 36 min.

Since, in 1 min the slower pipe can fill 'l'/x litres of the tank's capacity(In x min 'l' litre), and

In 1 min the faster one can fill 'l'/(x/3) litres of the tank's capacity(In x/3 min 'l' litre).

Therefore, in 36 min slower pipe will fill 36*('l'/x) liters, And
In 36 min faster pipe will fill 36*('l'/(x/3)) liters.

Since, both the pipes are contributing in filling the tank of capacity 'l' Litres.

Therefore,

36*('l'/x) + 36*('l'/(x/3)) = 'l'.

('l'/x) + ('l'/(x/3)) = 'l'/36.

(1/x) + (1/(x/3)) = 1/36.

(1/x) + (3/x) = 1/36.

Hope, it will be clear now.

If a is times faster then b and takes less minutes then in how many time they will fill tank.

Above answer is right 144 mins.

How when the tank was empty by one slow pipe (B) & 3 times faster pipe then slow its called pipe (A).

Know imagine the tank contain 4 liters of water and time taken to empty is 36 min.

As per above condition the B pipe can take 1 liter of water is 36 min mean the A pipe will take 3 liters at the time (3 times more than B. So 3x1=3).

If the pipe A as been removed the work as gone for B. But the B is 3 times slower.

Now A pipe as take 36 min for 3 liter means B will take 3 times more time 108 min (36x3=108).

Already the pipe B was have taken 36 min (for 1 liter) and adding the 108 min for balance 3 liter after adding the answer was 144 min.

(or).

For 1 liter it take 36 min means for 4 liter its 144 min as per above calculation.

Let's A = Fast pipe.

B = Slow pipe.

A takes x time. And B takes 3x time.

So, in 1 min. 1/x + 1/3x = 1/36.

By solving. 4x/3x^2 = 1/36.

Finally x = 4*36/3.

x = 48.

Time taken by slow pipe = 3x = 3*48 = 144 min.