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How many litres of a 12 litre mixture containing milk and water in the [#permalink]
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Bunuel wrote:
How many litres of a 12 litre mixture containing milk and water in the ratio of 2 : 3 be replaced with pure milk so that the resultant mixture contains milk and water in equal proportion?

A. 1.0 litres

B. 1.5 litres

C. 2.0 litres

D. 4.0 litres

E. 4.0 litres


This question can be approached in multiple ways, so I'm trying to solve this using "Allegation and mixture".

(Initial qty milk) \(\frac{2}{5}= 40\) % ------------------\(\frac{1}{1} = 100\) %(adding milk)
---------------------------------------\(50\) %-------------------------
\(100 - 50 = 50 \)-----------------------------------------\(50 - 40 = 10\)

Ratio \(\frac{50}{10}\) = \(\frac{5}{1}\)

Total is;\((5+1) or, \)
\( 6------>12\)
\(1 ------>\frac{12}{6}=2\)

Extra milk added in the solution is \(2\) liters. Ans C

Originally posted by meanup on 11 Dec 2020, 21:21.
Last edited by meanup on 17 Dec 2020, 22:11, edited 1 time in total.
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Re: How many litres of a 12 litre mixture containing milk and water in the [#permalink]
In my approach it should be 2.4 litre. In the 12 ltr mixture, there is 4.8 ltr milk and 7.2 ltr water. If we calculate mathematically, 2.4 ltr milk should be added. Then the total mixture will be 14.4 ltr. Half of 14.4 ltr is 7.2. what's wrong in my method?

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Re: How many litres of a 12 litre mixture containing milk and water in the [#permalink]
kris19 wrote:
Hea234ven wrote:
In my approach it should be 2.4 litre. In the 12 ltr mixture, there is 4.8 ltr milk and 7.2 ltr water. If we calculate mathematically, 2.4 ltr milk should be added. Then the total mixture will be 14.4 ltr. Half of 14.4 ltr is 7.2. what's wrong in my method?

Got it.. i missed the thing'replacement' in the question

Posted from my mobile device


From 12 ltrs, x ltrs are taken out, so (12-x) ltrs of mixture are remaining.
In this (12-x) ltrs, milk will be 2/5*(12-x) and water will be 3/5*(12-x)
Now, for this (12-x) ltrs of mixture, x ltrs of pure milk are added, so
milk = 2/5*(12-x)+x, and
after adding x ltrs of pure milk to (12-x) ltrs, the final (resultant) mixture will be 12 ltrs.
Now, 2/5*(12-x)+x = 1/2*(12) [this is the resultant mixture, in which milk to water ratio is 1:1, so 6 ltrs of milk and water]
solving for x, we get x = 2 ltrs.
Answer (C)
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How many litres of a 12 litre mixture containing milk and water in the [#permalink]
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Milk= (2/5)*12= 4.8 L
Water= I don't care {It's better if you go on solving with one of the quantities in the mixture without doing unnecessary calculation}

Suppose I remove x litre of solution. It means x consists of 2/5 x of milk and 3/5 x of water
also, i am adding the same quantity of pure milk, which consist 1/1 x of milk i.e. x

=4.8-(2/5 x) + (x)

Resultant solution in in equal proportion; milk will be 6 L (total is 12)

Therefore, 4.8-(2/5 x) + (x) = 6 L

x= 2 L
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Re: How many litres of a 12 litre mixture containing milk and water in the [#permalink]
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Bunuel wrote:
How many litres of a 12 litre mixture containing milk and water in the ratio of 2 : 3 be replaced with pure milk so that the resultant mixture contains milk and water in equal proportion?

A. 1.0 litres

B. 1.5 litres

C. 2.0 litres

D. 4.0 litres

E. 4.0 litres

Solution:

Let’s focus on the amount of milk in the solution, which has an initial concentration of 2/5 = 0.4. Thus, we start with 12 * 0.4 = 4.8 liters of milk in the solution. Then we remove x liters of solution that has a concentration of 0.4 milk. We then replace those x removed liters with pure milk with a concentration of 1.0 (i.e. 100% milk). The result is 12 liters of solution with a 0.5 concentration of milk.

We can put all this information into an equation:

(12 * 0.4) - (0.4 * x) + (1.0 * x) = 12 * 0.5

4.8 - 0.4x + x = 6

0.6x = 1.2

x = 2

Answer: C
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Re: How many litres of a 12 litre mixture containing milk and water in the [#permalink]
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The key thing to understand here is the amount of mixture that is being taken out contains both water and milk
Let X be the amount of mixture taken out and replaced with pure milk -

2/5*12 - 2/5*(X) + X = 3/5*12 - 3/5*(X)

Here - 2/5*12 is the total amount of milk in the mixture
2/5*X - is the amount of milk part of the mixture taken out
3/5*12 is the total amount of water in the mixture
3/5*X - is the amount of water part of the mixture taken out

Solving for X, we will get the answer as 2
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Re: How many litres of a 12 litre mixture containing milk and water in the [#permalink]
How come I get this wrong if I do this:

Final/Initial = (1 - b/12) ^1
1/1 / 3/5 = 12 - b /12
5/3 = 12 - b / 12
24 = -3b
b = -8

Where Final/initial is the final concentration of water and initial concentration.
b is the volume to be replaced and what we are looking for.
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Re: How many litres of a 12 litre mixture containing milk and water in the [#permalink]
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Bunuel wrote:
How many litres of a 12 litre mixture containing milk and water in the ratio of 2 : 3 be replaced with pure milk so that the resultant mixture contains milk and water in equal proportion?

A. 1.0 litres

B. 1.5 litres

C. 2.0 litres

D. 4.0 litres

E. 4.0 litres



Milk and Water: 24/5 and 36/5 respectively.

Since the solution is being replaced with Milk, we will find out for Water:

final conc is half and half i.e. milk and water should be equal, 6 =36/5*(1-b/12) (b here is the amount being replaced)

Solving for b gives 10=12-b= 2.0 litres.
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Re: How many litres of a 12 litre mixture containing milk and water in the [#permalink]
Since the solution is being replaced with milk, we will work on water. initial volume of water 3/5*12=36/5 =7.2 liter and in the final mixture volume of water=1/2*12 =6 L
Since a portion of the mixture was removed and replaced with pure milk total volume remain unchanged i.e 12 L
So (7.2-6.0) = 1.2 L water must be removed. 7.2 L water was in 12 L mixture so 1.2 L water will be in 12/7.2*(1.2)=144/72=2 L So 2L of mixture should be removed
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Re: How many litres of a 12 litre mixture containing milk and water in the [#permalink]
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