A 100-litre Mixture of Milk and Water Contains 36 litres of Milk GMAT Problem Solving

Question: A 100-litre mixture of milk and water contains 36 litres of milk. 'x' litres of this mixture is removed and replaced with an equal amount of water. If the process is repeated once, then the concentration of the milk stands reduced at 25%. What is the value of x?

A) 17.5 litres
B) 16.67 litres
C) 17.67 litres
D) 16.5 litres
E) 16 litres

“A 100-litre mixture of milk and water contains 36 litres of milk." - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The GMAT Quant topic's problem-solving section comprises highly calculative mathematical problems that must be solved using the appropriate mathematical facts.

Answer: B

Solution and Explanation:

Approach Solution 1:

Given in the question that 100 liters mixture has 36 liters of milk. Rest is water. X liters of this mixture is removed and replaced with equal amount of water. If this is done once the concentration of milk reduces to 25%. It has asked to find out the value of x.

To solve this we should understand that, you are removing a part of the solution and adding water. The quantity of milk stays the same even after you add water.

C1*V1 = C2*V2

This is repeated once more.

C2 = C1 * (V1/V2)^2

0.25 = 0.36∗[(100−x)/100]2.25= 0.36∗[(100−x)/100] *2

(100−x)/100=5/6

x = 100/6 = 16.67 litres
Hence, B is the correct answer.

Correct Answer: B

Approach Solution 2:

Given in the question that 100 liters mixture has 36 liters of milk. Rest is water. X liters of this mixture is removed and replaced with an equal amount of water. If this is done once the concentration of milk reduces to 25%. It has asked to find out the value of x.

Short trick -

For replacement problems

C(Final) / C(Initial) = (1−x/y)^n

Where C is the concentration
x is the amount replaced
y is the total amount
and
n is the number of replacement

Therefore for the given problem
(25/36) = (1−x/100)^2
Take Square root on both sides
5/6 = (1- x/100)

x= 16.67 litres
Hence B is the correct answer.

Correct Answer: B

Approach Solution 3:

Given in the question that 100 liters mixture has 36 liters of milk. Rest is water. X liters of this mixture is removed and replaced with an equal amount of water. If this is done once the concentration of milk reduces to 25%. It has asked to find out the value of x.

36 L of milk and 64 L of water are in a 100 L combination.
As a result, M and W are 9:16 in ratio. x L of solution have been eliminated.

As a result, we have 64-16/25x water and 36-9/25x milk.
For ease of calculation, multiply 9/25x by 4 and divide the result to get 36/100x.

Since this procedure is repeated 2 times.
This is the equation
25=36*(36-36/100x)^2)/(36)^2

By solving it.
We get x=100/6 OR 50/3 OR 16.67
Hence B is the correct answer.

Correct Answer: B

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