Aptitude - Pipes and Cistern - Discussion

Pipe A fills tank in 6 hours, pipe B in 8 hours. Both pipes opened simultaneously, then after how many hours should pipe B should be closed so that tank is filled in 4 hours.

I am getting a negative value and answer I am getting is 16/3 which is wrong. Please help.

It is easy. It is given that the cistern will be filled in just 30 minutes. And we don't know that who between A and B takes how much time from 30 minutes to fill the tank.

Suppose A takes x minutes. Then B will take (30-x) minutes.

But here is given that B is turned off in some time. We don't know when. So take it as Y minute. After Y minute only A will fill remaining part in 30-Y minute.

So first A+B will fill for Y minute and then B is turned off. So only A will fill in 30-Y minute.

So the equation is (A+B)Y + A(30-Y) = 30 minute.

@Rohit are you kidding bro?

If A and B take more than 4 hours to fill the tank (they takes 6 and 8 hours). Then how could anyone of them fill it in 4 hours. Use some mind.

@Rohit.

Is the answer 3?

Why x is multiplied by total work?

I'm here with an easy solution.

In 1 min A fill 2/75 of tank. In 30 min A fill 30*2/75 = 4/5 of tank since A is turned on for 30 min while B is shut after few mins that we have to find:

Now tank which B will fill in x min = 1-4/5 = 1/5.

Now work/work in 1 min = Total no. of min (x).

(1/5)/(1/45) = x.

So x = 9 min.

Let A one min work = 1/37.5 = 2/75.

Let B one min work = 1/45.

Let B turn off after x min.

And so tank filled in 30 min.

So Tank full = Part filled by A and B + Part filled by only A.

1 = (A+B)x+(30-x)A.

1 = 11x/225+(30-x)2/75.

That's way x = 9.

Both together can do a work in 225/11 minute.

Now pipe A can do a work in 75/2 minute. He alone did work for 30 minutes in last.

30*2/75=4/5.

Now 1/5 had been filled by a and b together. 1 cistern in 225/11 minutes then 1/5 in how many minutes ?

Simply put A can fill in 75/2 minutes.

Therefore in 1 min it fills 2/75 part.

Therefore in 30 min it will fill 2*30/75 = 4/5th part.

Now after 30 min amount remaining to be filled will be 1-4/5 = 1/5.

(In above subtraction 1 means whole cistern), so now B has to fill 1/5 i.e. remaining part. Question is how many minute does B takes to fill 1/5 part of the cistern.

We know from question that B takes 45 min to fill the cistern.

Therefore in 1 minute fill 1/45th part.

Therefore x *1/45 = 1/5 (where x= minute it actually takes to fill the cistern).

Solving X = 9 minutes.

Nice explanation @Mahesh Patil. Thank you.