A Milk Vendor Has 2 Cans of Milk. The First Contains 25% Water and The GMAT Problem Solving

Question: A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?

4 litres, 8 litres
6 litres, 6 litres
5 litres, 7 litres
7 litres, 5 litres
8 litres, 7litres

Correct Answer: B

Solution and Explanation
Approach Solution 1:
Given:

Number of cans of milk that the vendor has is 2.
The first contains 25% water and the rest milk.
The second contains 50% water.

Find Out:

How much milk should he mix from each of the containers so as to get 12 litres of milk
Given that the ratio of water to milk is 3 : 5

Let us match up the percentages of water in the two milk mixtures with the ratio that we want to achieve.

The ratio of water to milk that we want to achieve is 3:5.

If we add up the ration, the total is 8

Since the ratio is 3:5, the required amount is 3/8 water and 5/8 milk.

Now, we will focus on the water, since, if 3/8 of the mixture is water, the other 5/8 will have be milk.

As per the problem statement, the mixes are 25% water and 50% water. Let us express them in 8ths as well.

We get:

The first mix is 2/8 water.
The second mix is 4/8 water.

Now, we are looking for 3/8 water, and since 3/8 is halfway between 2/8 and 4/8, this answer becomes easy for us.

By using allegation, we can determine that we have to use equal amount of water and milk.

As per the options provided only option B has equal amounts which is 6 litres to 6 litres.

Hence, the correct answer is (B).

Approach Solution 2:

Algebraic Solution:

Given:

Number of cans of milk that the vendor has is 2.
The first contains 25% water and the rest milk.
The second contains 50% water.

Find Out:

How much milk should he mix from each of the containers so as to get 12 litres of milk
Given that the ratio of water to milk is 3 : 5

We want 12 liters of milk such that the ratio of water to milk is 3 : 5

In other words, we want the resulting mixture to be 3/8 water

Let x = the volume of 25% water needed

So, 12 - x = the volume of 50% water needed (since we want a total volume of 12 liters)

So, the total volume of water in the mixture = 0.25x + 0.5(12 - x)

Since we want the resulting 12-liter mixture to be 3/8 water, we can write:

[0.25x + 0.5(12 - x)]/12 = 3/8

By simplifying numerator: (6 - 0.25x)/12 = 3/8

Cross multiply: 48 - 2x = 36

Solve: x = 6

So the answer is 6 litres of milk and 6 litres of water. Hence, the correct answer is B.

Approach Solution 3:
Let x and (12-x) litres of milk be mixed from the first and second container respectively
Amount of milk in x litres of the the first container = .75x
Amount of water in x litres of the the first container = .25x
Amount of milk in (12-x) litres of the the second container = .5(12-x)
Amount of water in (12-x) litres of the the second container = .5(12-x)
Ratio of water to milk = [.25x + .5(12-x)] : [.75x + .5(12-x)] = 3 : 5

⇒(.25x+6−.5x)/(.75x+6−.5x)=3/5⇒(6−.25x)/(.25x+6)=3/5⇒30−1.25x=.75x+18⇒2x=12⇒x=6
Since x = 6, 12-x = 12-6 = 6
Hence 6 and 6 litres of milk should mixed from the first and second container respectively

“A milk vendor has 2 cans of milk. The first contains 25% water and the”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official Guide for GMAT Review". To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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A Milk Vendor Has 2 Cans of Milk. The First Contains 25% Water and The GMAT Problem Solving

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