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

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The proportion of milk and water in 3 samples is 2 : 1, 3 : 2 and 5 :  [#permalink]

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16 May 2020, 01:07
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Difficulty:

45% (medium)

Question Stats:

65% (02:33) correct 35% (02:23) wrong based on 54 sessions

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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

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

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Re: The proportion of milk and water in 3 samples is 2 : 1, 3 : 2 and 5 :  [#permalink]

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16 May 2020, 01:29
3
LCM[(2+1), (3+2), (5+3)] = 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

GMATinsight wrote:
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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Joined: 19 Mar 2014
Posts: 5
Schools: AIM '17
Re: The proportion of milk and water in 3 samples is 2 : 1, 3 : 2 and 5 :  [#permalink]

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16 May 2020, 02:25
2
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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Re: The proportion of milk and water in 3 samples is 2 : 1, 3 : 2 and 5 :  [#permalink]

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16 May 2020, 02:38
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
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The proportion of milk and water in 3 samples is 2 : 1, 3 : 2 and 5 :  [#permalink]

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16 May 2020, 02:51
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 = $$\frac{227}{133}$$
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Joined: 02 Feb 2020
Posts: 2
Re: The proportion of milk and water in 3 samples is 2 : 1, 3 : 2 and 5 :  [#permalink]

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16 May 2020, 03:46
1
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)
= [(80+72+75)/120] / [(40+48+45)/120]
= 227/133

That is option D, the answer.
Re: The proportion of milk and water in 3 samples is 2 : 1, 3 : 2 and 5 :   [#permalink] 16 May 2020, 03:46