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Ilham23
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M05-23 15 Sep 2024, 12:27
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I think this is a high-quality question and the explanation isn't clear enough, please elaborate. I do not understand why you denote the rate of the second case with (x-3). Since it takes 3 more liters to empty, does not it have to be (x+3)?
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M05-23 15 Sep 2024, 12:30
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Ilham23
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. I do not understand why you denote the rate of the second case with (x-3). Since it takes 3 more liters to empty, does not it have to be (x+3)?
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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.
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M05-23 17 Mar 2025, 04:12
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I like the solution - it’s helpful.
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M05-23 16 Apr 2025, 22:15
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I solved using a matrix

RateTimeWork
DrainC/463c/2
Rain3618
Total6C


[3c][/2] - 18 = C

3c-2c=36

C=36
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M05-23 05 May 2025, 15:14
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M05-23 24 May 2025, 00:01
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M05-23 05 Jun 2025, 19:47
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Concept: Draining will have negative work.
Method 1: Let D be the rate of draining pe hour.
We have (3ltr/hr - D) *6 = -D*4 as capacity is same.
Solving this, we get
18 -6D = -4D,
2D=18, D=-9
C= -C*4 = - (-9) *4 = 36

Method 2: Let work unit be 12 LCM of (4,6)= 12
Through this we get rate equation,
D=-3
D+R=-2
R=1 ltr/hour. However, we know that rain is adding water at the rate of 3ltr/hr.
When R= 1, D=-3
When R=3, D= -9
C= 9*4= 36 or 6*6
C=36

Method 3:
-C/4 +3 = -C/6
2C/24=3
C=12*3 = 36

Method 4:
Rain fills 6*3= 18 ltrs of bucket in 6 hours at the rate of 3ltr/hr.
Therefore,
-(C+18)/6 = -C/4
2C+36=3C
C=36

I always consider draining as -ve so as to avoid confusion while solving question with draining and filling pipe
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M05-23 16 Jun 2025, 03:07
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Bunuel
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Official Solution:

A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool?

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. Then the capacity of the tank will be \(C=time*rate=4x\);

Now, when raining, the net outflow is \(x-3\) liters per hour, and we are told that at this new rate the pool is emptied in 6 hours. So, the capacity (C) of the pool also equals to \(C=time*rate=6(x-3)\);

Thus we have: \(4x=6(x-3)\). Solving gives \(x=9\). Therefore \(C=4x=36\).


Answer: D
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.

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.
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hi Bunuel, does almost all question I did i did not cared about magnitude took ouflow as -ve and inflow as positive why i am getting wrong with this logic here?
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M05-23 16 Jun 2025, 06:17
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Sushi_545

hi Bunuel, does almost all question I did i did not cared about magnitude took ouflow as -ve and inflow as positive why i am getting wrong with this logic here?
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Your question isn’t fully clear. Are you using a method where inflow is positive and outflow is negative?

In this problem, we’re using the formula capacity = time * net rate, and the capacity stays the same in both cases. The net rate is already adjusted to reflect outflow and inflow, which is why it's written as x - 3. The minus sign is used because the rain works against the draining.
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M05-23 16 Jun 2025, 06:29
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Bunuel
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hi Bunuel, does almost all question I did i did not cared about magnitude took ouflow as -ve and inflow as positive why i am getting wrong with this logic here?

Your question isn’t fully clear. Are you using a method where inflow is positive and outflow is negative?

In this problem, we’re using the formula capacity = time * net rate, and the capacity stays the same in both cases. The net rate is already adjusted to reflect outflow and inflow, which is why it's written as x - 3. The minus sign is used because the rain works against the draining.
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Hi Bunuel,

I meant to say i arrived at using 3-x and in every question i solved just like these i took outflow aa negative and inflow as positive and got the correct answer. Dont know here why my answer came wrong. X litres say 10 litre are flown out and 3 litres flown in so 10-3 or 3-10 either way we are getting effective capacity to be 7 cant take negative as capacity cant be negative so where i did wrong?
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M05-23 16 Jun 2025, 06:33
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Sushi_545
Bunuel
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hi Bunuel, does almost all question I did i did not cared about magnitude took ouflow as -ve and inflow as positive why i am getting wrong with this logic here?

Your question isn’t fully clear. Are you using a method where inflow is positive and outflow is negative?

In this problem, we’re using the formula capacity = time * net rate, and the capacity stays the same in both cases. The net rate is already adjusted to reflect outflow and inflow, which is why it's written as x - 3. The minus sign is used because the rain works against the draining.



Hi Bunuel,

I meant to say i arrived at using 3-x and in every question i solved just like these i took outflow aa negative and inflow as positive and got the correct answer. Dont know here why my answer came wrong. X litres say 10 litre are flown out and 3 litres flown in so 10-3 or 3-10 either way we are getting effective capacity to be 7 cant take negative as capacity cant be negative so where i did wrong?
Show more

In this case, the pool is being emptied, so the net rate must be positive outflow. That means the draining rate must be greater than the rain rate.

So if you write net rate as 3 - x, you'd get a negative value, which doesn't match the context (pool getting emptied). That's why the correct expression is x - 3.
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I like the solution - it’s helpful. 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.
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M05-23 29 Aug 2025, 04:41
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