Aptitude - Pipes and Cistern - Discussion

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.

Here, given problem is that,

First half of the tank is filled in 3hrs by using only 1 tap.
After that 3 more pipes are opened so, now total working pipes 4(they are similar means takes the same time to fill the tank).

The remaining we have 6 - 3 = 3hrs.
3hrs means = 3 * 60 = 180min
So, equally this time shared by 4 pipes 180/4 = 45 min.
So total time is 3hrs 45 min.

I think logic behind 2/3 :3::1:x is;

X is the time taken by 4 tap to fill remaining 1/2 in hours.
AND, 2/3 part of tank is filled in 1 hour.
So, (2/3)/(1/2) = 1hr/xhr
Which can b also written as
2/3 : 3 :: 1.

To verify put 45 in place of X and check if the ratio r equal or not(deal in minutes what I mean is that conversation 1hr into 60 minute.

So, 1/x becomes 60/45 that is 4/3. And also, 2/3 : 1/2 is 4/3.

The first tank will take 3hrs to fill in half of the tank.

4 tanks will take 6/4=1.5hrs to fill the full tank.
but as half of the tank is already filled, it will take 0.75hr=45mins for the rest half tank.

It will take less than 24 hours. How?

It should be:

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