## Milk Mixture

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### Milk Mixture

by lkm » Mon Aug 02, 2010 6:31 pm
Question:

A container contains 40 liters of milk. From this container 4 liters of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?

A) 26.35 liters
B) 27.36 liters
C) 28 liters
D) 29.16 liters
E) 29.26 liters
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by [email protected] » Mon Aug 02, 2010 7:05 pm
Initially quantity of milk was 40 liters.
Now 4 liters of milk was removed and replaced with 4 liters of water.
So we are now having 36 liters of milk and 4 liters of water.
So ratio of milk is to water is 36:4 = 9:1.
So next time when 4 liters is being removed, it has 4*9/10 parts of milk and 4*1/10 parts of water.
So now the quantity of milk is 36 - 4*9/!0 = 36*9/10 and quantity of water is 4 - 4*1/10 = 4*9/10.
We are adding 4 liters of water.
So the changed quantity of water is 4*9/10 + 4 = 4*19/10.
Or ratio of milk to water is now 36*9/10 : 4*19/10 = 81:19.
So, the second time when 4 liters is being removed, quantity of milk in that is 4*81/100.
Or the net quantity of milk is now 36*9/10 - 4*81/100 = 29.16 liters

The correct answer is D).
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by indiantiger » Mon Aug 02, 2010 7:10 pm
[email protected],

amazing explanation. I knew the shortcut formula and but your explanation really helps in understanding the shortcut formula.

The formula is

x{1- y/x}^n

here x is the original liquid
y is the amount of liquid taken out
n is the number of times taken out

so 40 {1-4/40}^3
40 * 9/10 * 9/10 * 9/10 = 29.16
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by deeyah » Mon Aug 02, 2010 7:12 pm
lkm wrote:Question:

A container contains 40 liters of milk. From this container 4 liters of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?

A) 26.35 liters
B) 27.36 liters
C) 28 liters
D) 29.16 liters
E) 29.26 liters
Container initially contains 40 lts of milk and no water.
4 lts of milk was taken out means we are left with 36 lts of milk and 4 lts of water was added.But the qty is still 40

Now again the same process is repeated but ratio of milk and water is 9:1
If 4 lts of the mixture is drawn out , the quantity of milk will be (9/10 )x4 =3.6 lts of milk and rest water.

The second time the process is repeated but now the ratio of milk and water again changes.
Qty of milk now is 36-3.6 lts=32.4 lts .Rest is water..
Now we take out another 4 lts of the mixture then amout of milk in it will be (32.4/40)x4=3.24

Hence the qty of milk left =32.4-3.24=29.16 lts

Q

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