Aptitude - Pipes and Cistern - Discussion

C is twice fast as B.
B is twice fast as A.
So, speed here If A = x, B = 2x, C = 4x.
Is speed increases time decrease. As we know from the above speeds we can get the value of time. B is twice fast as A. It mean just think speed multiplies. But time it should be divided.

So, If A takes x hour then B takes less time. It mean x/2. Similarly, C is twice fast as B. It mean if B takes x/2hr. Then C takes less than B as x/4.

So finally A takes x hr, B takes x/2 hr, and C takes x/4 hr.

Basically they have used the concept of speed is inversely proportional to time. The question talks about how fast the pipes can fill the tank. Given that ratio, we inverse it to find the time.

So, A takes x hrs, B will take X/2 hrs because it is twice as fast as A and C will take x/4 hrs.

Now summation of work done by each pipe in 1 hr = (1/x+2/x+3/x) =7/x=1/5;.

So, from here x=35.

As per the question we can solve as:
c=2b;-------->1.
b=2a;-------->2.

Also a+b+c=1/5(work done in 1 hour by a,b,c)--------?3.

Now substitute the value of c=2b and b=2a in 3.
So eqn.3 becomes a+2a+2b = 1/5.

Again substitute b=2a in place of b.
So eqn becomes 3a+4a = 1/5.

So solving we get the value of a = 1/35.
So that is d work done in 1 hr.
So total work done = 35.

The pipe C is twice as fast as B.
Means ratio of C:B = 2:1.
B is twice as fast as A.
Means B:A = 2:1.
Combine ratio of A:B:C = 1:2:4.

NOW,
The tank is filled in 5 hours by A,B,C.
so the addition of ratio =7(total parts of the tank)
So, 7*5 =35 hours to fill.
Now we have to find A's time.
A's ratio is 1. So divide 35by 1 =35 is the answer.

@Savitha.

We know that capability of A, B, C.
More capability takes less time to complete the work. it means that strengths is inversely proportional to time.

A + 2A + 4A inversely to x/5(x is some constant)
X = 5*7A .......35A.
35A part work done in......1 hour.
A's total work.................?
So, ? =35hrs.

Try to understand question, question itself has answer.

Let A fill tank in x hrs.

Therefore tank filled in one hrs is 1/x.

And B pipe is twice than A means 2 (1/x).

C pipe is twice than B means 2 (2 (1/x) ) i.e 4/x.

1/x+2/x+4/x = 1/5.

7/x = 1/5.

x = 35 hrs.

As pipe C is twice as fast as B and B is twice as fast as A so if a fill the tank in x min.

As B is Two Time Faster not slower so it will take half time less than A that's why we have taken pipe B will fill in x/2 hours in less time compared to A.

1/5 is taken wrt to 1 hr but not A B C they are taken as A, 2A, 4A which has to to be taken wrt 1hr but in equation how are they equating A, 2A,4A to 1/5 in an equation. if we want to solve an equation it should be write to 1 hr only.

[A + B + C] = 1/5.
According to question;
C = 2B = 4A----------- 2(2A )= 4A.
B = 2A.
[A] = ?

A + B + C = 1/5.
A + 2A + 4A = 1/5,
7A = 1/5,
A = 1/7 * 5,
A = 1/35 ==> 35hr.

The question is say that The pipe C is twice as fast as B and B is twice as fast as A i.e means A:B:C = x:2x:4x respectively then why you are take 1/x, 2/x, 4/x.