How many litres of a 12 litre mixture containing milk and water in the

Question

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. 5.0 litres

kris19 · Accepted Answer

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)  
solving for x, we get x = 2 ltrs.
Answer (C)

ScottTargetTestPrep · Answer

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

shades28 · Answer

Options D and E are the same. Could you please edit the question?
Thanks in advance.

Posted from my mobile device

imeanup · Answer

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

Hea234ven · Answer

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

Posted from my mobile device

Hea234ven · Answer

Shadyshades · Answer

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

somyamehta777 · Answer

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

CEdward · Answer

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.

PRI23YA · Answer

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.

KB1920 · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

How many litres of a 12 litre mixture containing milk and water in the

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

How many litres of a 12 litre mixture containing milk and water in the

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards