Aptitude - Pipes and Cistern - Discussion

1 pipe takes 6 hrs to fill the tank.
So 1 pipe take 3 hrs to fill half the tank.
Other half is filled with 4 pipes,
The part of the tank filled with 4 pipes in 1 hr = 4 * 1/6 = 2/3.

So, the time taken to fill half the tank = (1/2) / (2/3)= (1/2) * (3/2) = 3/4 hrs= 45 minutes.
So the total time = 3hrs 45 minutes.

Thanks @Vicky.

Thanks @Vicky. That was clear and simple.

Simple.

Tank takes to fill within 6 hours. So half of the tank we stop the waterfall. So half tank fills times 3 hours. So remaining half tank we use 4 pipes. Each pipes s similar so each pipe takes 3 hours to fill the tank. But here we open together all pipes.

The remaining 3 hours will be reduced by 4 pipes. 3 hours =180mins.
So we know 180/4 pipes = 45mins. So already half tank is filled.
Remaining the half tank has been filled withn 45 mins so, 3hours 45 mins is the answer.

1. Time taken by a pipe to fill half the tank = 3 hrs.

2. So, time taken by 1st pipe along with 3 other similar pipes (i.e 4 pipes).

= 3 hrs/4.

= 180 min/4.

= 45 min.

Adding 1 and 2,

Total time taken = 3hr 45 min.

2/3:1/2::1:x.

X = (1/2*1*3/2) = 3/4.

I did not got these two steps shall you explain me please in this step what is X why we should take the ratio.

One tap can fill tank completely in 6 hr.

Actually, tap's 1 hr work = 1/6.

--> Also, one tap can fill tank half in 3 hr.

--> When there are 3 more similar taps. Then total taps = 4.

4 tap's 1 hr work = 4/6.

Adding,

-->3/6 (since tap is filled half i.e. for 3 hrs by 1st tap) + x*4/6 = 1.

--> x because remaining x hr will be taken by 4 tap's to fill other half tank. Not necessarily 3 hr. That was taken by 1st tap alone.

On solving.

-->x = 3/4.

Getting total time = 3 hrs (tank filled half by 1st tap) + x.

--> 3+3/4.
-->15/4.
-->3:45 min.

If 1 tap takes 6 hours --> 2 taps takes 6/2=3 (half time as fill faster).

If 2 taps takes 6/2=3 (half time)---4 taps takes 3/2=1.5 (i.e 1:30 min).

1:30 min= 60 min +30 min= 90 min.

90 min (time taken by 4 tapes to fill full tank).

But left is only half tank.

So 90/2 = 45 min.

Now total time = 3hour+45 min.

1 tap takes 6 hours.

2 taps will take 3 hours.

Similarly 4 taps will take one and half hour i.e. 90 minutes to completely fill the tank.

Therefore, for half part it will take 45 minutes.

First tap will take 3 hours to half fill the tank.

Hence, we get 3 hours 45 minutes as answer.

45 min are calculated as 3/4*60 = 3*15 = 45 min.

i:e 3/4 of 60 min(1 hr).