The proportion of milk and water in 3 samples is 2 : 1, 3 : 2 and 5 :

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

A) 2 : 1
B) 5 : 1
C) 99 : 61
D) 227 : 133
E) 237 : 123

nick1816 · Accepted Answer

LCM  = LCM(3, 5,8) = 120

Suppose we're mixing 120 units of each sample.

Amount of milk in resulting mixture  = \frac{2}{3}*120 +\frac{3}{5}*120 + \frac{5}{8}*120 = 80+72+75=227

Amount of water = 360-227 = 133

D

shreya5055 · Answer

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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PoojanB · Answer

LCM(2+1,3+2,5+3)=120
So lets say we got 120 L of each sample
amount of milk in each mixture = \frac{2}{3}*120+\frac{3}{5}*120+\frac{5}{8}*120 = 227 
 
Only option D satisfy this qty. (We can also calculate amt of water in each mixture and add them in similar manner shown above)

Ans D

lacktutor · Answer

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).

gmatlawyer · Answer

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

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

Similarly, quantities of water in each of the solutions would be 1/(2+1), 2/(3+2) and 3/(5+3).

Since the three solutions are mixed in equal quantities, we will divide the quantity of milk with the quantity of water, as follows:

(2/3 + 3/5 + 5/8) / (1/3 + 2/5 + 3/8)
=   /  
= 227/133

That is option D, the answer.

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