The Proportion of Milk And Water in 3 Samples is 2 : 1, 3 : 2 and 5 : 3 GMAT Problem Solving

Question: The proportion of milk and water in 3 samples is 2 : 1, 3 : 2 and 5 : 3. A mixture comprising equal quantities of all 3 samples is made. The proportion of milk and water in the mixture is

1. 2 : 1
2. 5 : 1
3. 99 : 61
4. 227 : 133
5. 237 : 123

Correct Answer: D

Solution and Explanation:
Approach Solution 1:
Given to us that the proportion of milk and water in 3 samples is 2 : 1, 3 : 2 and 5 : 3. A mixture comprising equal quantities of all 3 samples is made. It is asked to find the proportion of milk and water in the mixture.
This is a question of percentage and proportions.
Whenever there is a question of percentage and proportion, take the base amount to 100

Given in the first mixture
Milk and water are in the ratio of 2 : 1
For easy calculation consider the product of 3, 5, and 8 = 3 * 5 * 8 = 120 as the base sample.
(2 parts of milk + 1 part of water = 3 parts of the first sample)
Similarly in this way 5 and 8 are the other parts of the other sample.

Now firstly we’ll calculate the total quantity of milk and water of three given samples.

water content =\(\frac{1}{3}\)*120 +\(\frac{2}{5}\)* 120 + \(\frac{3}{8}\)* 120 = 40 + 48 + 45 = 133

The water content will be the total content - milk content
milk content = 120 * 3 - 133 = 227
It is asked in the question to find out the ratio of milk to water
Therefore, Milk : water = 227 : 133

Approach Solution 2:
Given to us that the proportion of milk and water in 3 samples is 2 : 1, 3 : 2 and 5 : 3. A mixture comprising equal quantities of all 3 samples is made. It is asked to find the proportion of milk and water in the mixture.
The amount of milk from each sample after mixing will be equal to one another.
1st sample has \(\frac{2}{3}\)x milk

2nd sample has\(\frac{3}{5}\)x milk

3rd sample has \(\frac{5}{8}\)x milk

We get,

\(\frac{2}{3}\)x + \(\frac{3}{5}\)x + \(\frac{5}{8}\)x = 3*x (a) where a = amount of milk in the mixture

(80 + 72 +75)/120 = 3*a

a = \(\frac{227}{360}\)

The amount of water will be 1 - a

Water = 1 - \(\frac{227}{360}\) = 133/360

The ratio of milk to water = 227: 133

Approach Solution 3:
The problem statement states that:
Given: 

• The proportion of milk and water in 3 samples is 2 : 1, 3 : 2 and 5 : 3.
• A mixture comprising equal quantities of all 3 samples is made.

Find out:

• The proportion of milk and water in the mixture.

The three ratios are 2:1, 3:2 and 5:3.

Therefore, the amount of milk in each of the solutions would be = 2/(2+1), 3/(3+2) and 5/(5+3);

Likewise, the amount of water in each of the solutions would be = 1/(2+1), 2/(3+2) and 3/(5+3).

Since the three solutions are combined in equal quantities, we will divide the amount of milk by the quantity of water. Therefore, we get:
(2/3 + 3/5 + 5/8) / (1/3 + 2/5 + 3/8)
= [(80+72+75)/120] / [(40+48+45)/120]
= 227/133

Hence, the proportion of milk and water in the mixture = 227 : 133.

“The proportion of milk and water in 3 samples is 2 : 1, 3 : 2 and 5 : 3”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT Problem Solving questions help the candidates to evaluate every data of the question to calculate the numerical problems effectively. It tests the candidates’ efficiency in analysing and solving quantitative problems. The candidates must have a solid knowledge of arithmetic, algebra and geometry in order to crack this GMAT Quantitative exam. GMAT Quant practice papers assist the candidates to go through several types of questions that will enable them to improve their mathematical knowledge.

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