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

A) 2 : 1
B) 5 : 1
C) 99 : 61
D) 227 : 133
E) 237 : 123
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Whenever a question is talking about percentages, take total as 100.
Similarly, whenever a question is talking about fractions, take total as product/ LCM of denominators.

Step 1: Here, in this ques, we need to first consider a quantity for three samples. For easy calculation, we will take product of 3,5&8 = 120 units of each sample.
(2 parts of milk + 1 part of water = 3 (total parts of first sample). Similarly, 5 & 8 are total parts of second & third samples respectively.

Step 2: Calculate the total quantity of milk/ water of three samples.
Water content:
=1/3*120 + 2/5*120+ 3/8*120
=40+48+45 = 133

Step 3: Calculate the amount of other content by subtracting first content from total.

Milk content:
=120*3 - 133 = 227

Step 4: Note carefully in the ques, which ratio is asked : milk to water or water to milk.
Final answer : Milk to water
227/133
Option D

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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

The amount of milk in each sample and all samples are equal to one another :
1st sample - \((\frac{2}{3})x\)
2nd sample - \((\frac{3}{5})x\)
3rd sample - \((\frac{5}{8})x\)

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

\(\frac{80+ 72 + 75}{ 120} = 3(a)\)

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

The amount of water = \(1- \frac{227}{360}= \frac{133}{360}\)

---> The ratio of milk to water = \(\frac{227}{133}\)
Answer (D).