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

Ilham23 · Answer

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)?

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.

RonWeasley4897 · Answer

I like the solution - it’s helpful.

cjcalero24 · Answer

I solved using a matrix

Rate 
 Time 
 Work 
 
  Drain 
 C/4 
 6 
 3c/2 
 
  Rain 
 3 
 6 
 18 
 
  Total 
  
 6 
 C

- 18 = C

3c-2c=36

C=36

jmaxr · Answer

I like the solution - it’s helpful.

anushree01 · Answer

I like the solution - it’s helpful.

btsaami · Answer

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

Sushi_545 · Answer

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?

Bunuel · Answer

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.

Sushi_545 · Answer

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?

Bunuel · Answer

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.

GuruDeshpande · Answer

I like the solution - it’s helpful.

kouassidrissa047 · Answer

I like the solution - it’s helpful.

SomeshParanjpe · Answer

I like the solution - it’s helpful.

Naman77701 · Answer

I like the solution - it’s helpful.

Prem6201 · Answer

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.

alrightalright · Answer

I like the solution - it’s helpful.

Chrisharley · Answer

I like the solution - it’s helpful.

Fisayofalana · Answer

I like the solution - it’s helpful. If we make the rate x and the bucket is drained in 4 hours, the work is 4x.

If we do the same for the 6 hours, the work is 6x.

There were 18 liters of rainfall (3 liters *6 hours) that needed to be additionally drained. I set up my equation like so:

6x = 4x + 18. I solved for x and got 9. The original capacity is 9*4 = 36

Advait01 · Answer

I like the solution - it’s helpful.

M05-23

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