Aptitude - Pipes and Cistern - Discussion

A pipe can fill the tank in 6 hours, so in 1 hour the pipe can fill 1/6 th part of the tank.

1 hour--------->1/6 part of tank.

3 hours--------->1/2 part of tank.

According to the data which had given in the question:The similar three more taps are opened so total number of taps are:4.

These four taps together in hour can fill (1/6+1/6+1/6+1/6=4/6=2/3) 2/3 part of the tank.

So, total time equals to 3.75 hours which is equals to 3 hours 45 minutes.

1 hour--------->1/6 part of tank.

3 hours--------->1/2 part of tank.

So 1/2 already filled and 1/2 has to be filled.

Now 4 similar taps are opened so total time taken is (1/6+1/6+1/6+1/6) =2/3.

Time to fill remaining 1/2 is 1/2=2/3*x.

X=3/4=.75.

Thus total time taken= 3 +.75 = 3.75.

1 tap has filled half of the tank in 3 hours and remained half of the tank have to be fill by 4 taps and we know that tank will take total 6 hours to fill. So, now remaining time is 3 hours that is 180 minutes and we have 4 taps so the solution is 180/4=45 min that is the tank taken total time is previous 3 hours that is filled by only 1 tap and by 4 taps is 45 mins.

So the total time is 3 hours and 45 mins.

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

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

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.

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.

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.

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.

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.

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.