Aptitude - Pipes and Cistern - Discussion

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.

It will take less than 24 hours. How?

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.

Thanks @Vicky. That was clear and simple.

Thanks @Vicky.

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.

Its pretty much a simple logic.

Tone tap 6 hrs to fill.

So 3 hrs to half fill.

A = 1/6.

4 taps 4a =4 * (1/6).

=> 2/3.

Now x be the tank capacity.

X/2 has filled already.

So remaining x/2 in 2/3.

X = 4/3 45 minutes.

So, totally 3 hrs 45 mts.

Considering the LCM of the all the four taps ie 6.

Now considering the capacity of tank be 6 units.

For the 1st half,

As only 1 tap is working so it fills 6/6 units/hr = 1 unit /hr (part filled by tap 1/total capacity of the tank).

As only 1 tap is working for the 1st half I.e. For 3 units of tank (total capacity of tank/2).

Calculations:

1 unit filled in 1 hr.

3 units filled in 3 hrs.

In second half 4 taps of same type are used, therefore it fills 4/6*6 = 4 units/hr (part filled by 4 taps/total capacity of the tank).

Now left out 3 units are filled by the combination of 4 taps.

Calculation:

4 units filled in 1 hr.

3 units filled in 3/4 hrs = 45 mins.

Therefore total time taken = time taken by 1st tap + time taken by combination of 4 similar taps.

= 3 hrs + 3/4 hrs = 3 hrs 45 mins.