M05-23

Question

A drain pipe can empty a bucket in 4 hours. On a rainy day, with the bucket full, the drain pipe manages to empty the bucket in 6 hours instead. If during the rainfall, the rain adds 3 liters of water each hour, what is the capacity of the bucket?

A. 9 liters
B. 18 liters
C. 27 liters
D. 36 liters
E. 45 liters

Show Answer

Official Answer

D

A. 9 liters
B. 18 liters
C. 27 liters
D. 36 liters
E. 45 liters

Bunuel · Accepted Answer

Official Solution:

A drain pipe can empty a bucket in 4 hours. On a rainy day, with the bucket full, the drain pipe manages to empty the bucket in 6 hours instead. If during the rainfall, the rain adds 3 liters of water each hour, what is the capacity of the bucket?

A. 9 liters
B. 18 liters
C. 27 liters
D. 36 liters
E. 45 liters

Show Answer

Official Answer

D

A. 9 liters
B. 18 liters
C. 27 liters
D. 36 liters
E. 45 liters

Let the rate of the draining pipe be  x  liters per hour. In this case, the capacity of the bucket can be represented as  C = time * rate = 4x .
 
On a rainy day, the net outflow is  x - 3  liters per hour, and it takes 6 hours to empty the bucket at this adjusted rate. Hence, the bucket's capacity (C) can also be expressed as  C = time * rate = 6(x - 3) .
 
Equating the two equations, we get:  4x = 6(x - 3) . Solving for  x , we find that  x = 9 . Consequently, the bucket's capacity is  C = 4x = 36  liters.

Answer: D

safwanst · Answer

Here's how I approached it.

Rain inflow is 3 l /hr
After 6 hours it would have filled in 18 l 
On top of this amount, the pipe would also have to drain the contents of the already filled pool.

We know that draining a filled pool takes 4 hours.
But draining a filled pool + the 18 l  takes 6 hours, hence it takes  2 hours to drain 18 l  .

Then do a ratio comparison:
If 18 l  takes 2 hrs, a filled pool takes 4 hrs.
18:2 = filled pool:4

Hence, filled pool = 36 l

It's also easier to just draw a diagram that would look something like this:
 
|__+18___| 2 hrs
|      x      | 4 hrs
|________|

From the diagram, it is more obvious that x is 36.

cemil1986 · Answer

other method
let x be the total capacity
x/4 equal to the drain rate. 3 equals rain inflow
6 hours rain inflow equals 18
x/4=(x+18)/6
6x=4x+72
2x=72
x=36

dakrownie · Answer

This is how I solved it.

Recall rate eqn: 1/r = 1/r1 + 1/r2

In this case, the rate is negative, hence, 1/r = 1/r1 - 1/r2

i.e. 1/6 = 1/4 - 1/r2

1/r2 = 1/4 - 1/6 = 1/12

Hence r2 = 12

W = RT 
C = RT = 3 * 12 = 36

manisha1234 · Answer

Instead of solving question with conventional method, solve it by plugging in the answer choices and out of the given answer choices 36 is the best to pick up.

filipTGIM · Answer

I appreciate all the methods mentioned but they involved a 2-step equation process.

I used this one involving only the rate equation :

Capacity of the pool : x litres
Draining pipe rate : x/4 --- x litres per 4 hours
Rain inflow rate : 3/1 --- 3 litres per 1 hour (negative in this case as draining is emptying and rain is filling the pool)
Group rate : x/6 --- x litres per 6 hours

Usual rate equation : 1/r1 + 1/r2 = 1/r ===> x/4 - 3/1 = x/6 ===> solve for x.

pacifist85 · Answer

I did it by calculating the reduction in rate, caused by the rain.

So, normally the drain pipe drains the full pool in 4 hours. This means that the draining rate is 1/4.
That rainy day, because the rain was filling the pool while the drain was emptying it, the pool was drained in 6 hours. This means that the draining rate was 1/6.

Now, 1/4-1/6 = 1/12. This must be the rate of the rain inflow. This means that the pool will be totally full in 12 hours (only by the rain).

So, 3 liters per hour is 3*12 = 36. Sounds complicated even to me that I solved it in this way, but sometimes it happens... So, is this way indeed correct?

sudipnayak93 · Answer

If you follow % efficiency method it will solved in seconds. The outlet pipe can drain the water in 4 days which mean its efficiency is 25% (divide 100 by 4) and when it rains its efficieny is reduced to 16.66% (divide 100 by 6) that means the rain is filling the pool at an efficiency of 8.33% (25%-16.66%). Now from the calculation we can deduce that the rain will take 12 hours to fill the pool (100/8.33%). So just multiply 12 with 3 and get the answer. This approach saves time but one needs to memorise the percentage to fraction conversion table. For example 12.5% =1/8.

manishtank1988 · Answer

My 2 cents: my 2 cents.png If you have any question, please let me know & i do like kudos

Kurtosis · Answer

Alternate approach:

Normal Time = 4 hours
Because of rain the pipe had to work for extra 2 hours.

Extra inflow to the pool = 3 * 6 = 18 litres

The pipe took 2 hours extra to drain out the extra 18 litres --> Rate = 18/2 = 9lt/hour

Total capacity = 9 * 4 = 36

Answer: D

meron · Answer

Hours to drain with no rain = 4 hrs 
Hours to drain with rain = 6 hrs
Hours to drain water from rain = 2 hrs
Water from rain = 3L/hr * 6hrs = 18L
Drain rate (I used only rain water) = 18L/2hrs = 9L/hr
Capacity (I used without rain) = 4hours * 9L/hr = 36L

sam12rawat · Answer

Hi  Bunuel  , I have a doubt here. I had subtracted the rate of the drainage pipe from the rate of the rain (3-x) instead of (x-3) because the pool is being filled and the rain is pouring in the same direction whereas the draining pipe is doing the opposite action. Could you please clarify where am I going wrong with this concept? Thank you.

Bunuel · Answer

We are told that on a rainy day, when the pool is full, the draining pipe is opened and  the pool is emptied  in 6 hours. So, even when raining the pool gets emptied, which means that outflow (draining rate) is more than the inflow.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Alessandro14 · Answer

Since the draining pipe can empty the pool in 4h, the draining pipe does 1 work in 4h (1/4h)
Working together (and contrasting the rain), the work is done in 6h (1/6h).

The right equation to solve: 1/4 - 1/x = 1/6 --> x=12 (so the rain takes 12h to fill the pool)

Since rain inflow into the pool is 3 liters per hour --> 3litre/h * 12h = 36 liters

rayt153 · Answer

Please kindly explain the part "On a rainy day, the net outflow is x− 3 liters per hour" X-3 and not x + 3 liters per hour - just trying to understand that bit.

Bunuel · Answer

The net  outflow  is "x - 3" liters per hour because the drain pipe empties x liters per hour, but the rain adds 3 liters back every hour. So, the effective  emptying rate  is the drain's rate minus the rain's addition.

Bunuel · Answer

Similar questions to practice: https://gmatclub.com/forum/m40-424805.html https://gmatclub.com/forum/m05-183668.html https://gmatclub.com/forum/m04-183659.html

Karmakar30 · Answer

Let the capacity of tank be x 
Rate of pipe = x/4 
Rate2 of the pipe = x/6 
Rate of filling the tank is 3 litre/hr 
Therefore, 
x/4-x/6=3 
x = 36 litre

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M05-23

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