In what ratio should Solution 1 and Solution 2 be mixed to

Question

In what ratio should Solution 1 and Solution 2 be mixed to get a solution which contains water and milk in the ratio of 3:7?

(1) Solution 1 contains water and milk in the ratio 1:9 and Solution 2 contains water and milk in the ratio 2:3
(2) The amount of milk in 100 gallon of solution 1 is 80 gallons more than that of water in the same solution. Further, 50 gallons of Solution 2 contains 10 gallons more milk than water.

Bunuel · Accepted Answer

(1) Solution 1 contains water and milk in the ratio 1:9 and Solution 2 contains water and milk in the ratio 2:3

Given:  \frac{w_1}{m_1}=\frac{x}{9x}  and  \frac{w_2}{m_2}=\frac{2y}{3y} , for some multiples  x  and  y .

We want  \frac{x+2y}{9x+3y}=\frac{3}{7} . Question:  \frac{x+9x}{2y+3y}=\frac{2x}{y}=?

From first equation we can express  x  in terms of  y  (or vise versa) substitute it in the second and get desired ratio:  \frac{x+2y}{9x+3y}=\frac{3}{7}  -->  y=4x  -->  \frac{2x}{y}=\frac{2x}{4x}=\frac{1}{2} . Sufficient.

(2) The amount of milk in 100 gallon of solution 1 is 80 gallaons more than that of water in teh same solulution. Further, 50 gallons of Solution 2 contains 10 gallons more milk than water.

Given:  w_1+m_1=100  and  w_1+80=m_1  --->  w_1=10  and  m_1=90  -->  \frac{w_1}{m_1}=\frac{x}{9x} ;

w_2+m_2=50  and  w_2+10=m_2  --->  w_2=20  and  m_1=30 -->  \frac{w_2}{m_2}=\frac{2y}{3y} ;

The same info as in (1). Sufficient.

Answer: D.

kamalkicks · Answer

answer is D

REMEMBER QUE IS ASKING RATIO 
 1. sufficent 
 equation will be like 
 1/10 x + 2/5 y = 3/10 (x+y)
 we can find ratio of x and y
2. sufficent similarly we can fin ratio
 ( READ ST 2 CAREFULLY)

hence D

gmatprep2011 · Answer

We need the ratio of both the liquids to get the answer
Statement 1 and Statement 2 independently give us this information
So answer D

subhashghosh · Answer

W/M = 3/7

W1/M1 = 1/9 W2/M2 = 2/3

So Q1/Q2 = (2/3 - 3/7)/(3/7 - 1/9)

= (14 - 9)/21/(27 - 7)/63 = 5/21 * 63/20 = 3/4

(1) is sufficient

(2)

For Solution 1

M = W + 80

M + W = 100

For Solution 2

M = W + 10

M + W = 50

So we can find the ratios of M:W in solutions and using above alligation technique find the required ratio.

Answer - D

Bunuel · Answer

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Zarrolou · Answer

Using aligation:

"get a solution which contains water and milk in the ratio of 3:7" => water = 30%

(1) Solution 1 contains water and milk in the ratio 1:9 and Solution 2 contains water and milk in the ratio 2:3 
Solution 2 (in terms of water): 40% 
Desired solution ( in % water):  30% 
Solution 1 (in terms of water): 10%

\frac{Solution_2}{Solution_1}=\frac{2}{1}

(2) The amount of milk in 100 gallon of solution 1 is 80 gallons more than that of water in the same solution. Further, 50 gallons of Solution 2 contains 10 gallons more milk than water. 
Solution 1: M=90 W=10 => 10% W
Solution 2: M=30 W=20 => 40% W, both statement give us the same info

Solution 2 (in terms of water): 40% 
Desired solution ( in % water):  30% 
Solution 1 (in terms of water): 10%

\frac{Solution_2}{Solution_1}=\frac{2}{1}

cumulonimbus · Answer

Hi Karishma,
Why is the ratio of S1 to S2 not equal to 1/2, by using this method:

W1/M1 = 1/9 W2/M2 = 2/3

So Q1/Q2 = (2/3 - 3/7)/(3/7 - 1/9)

= (14 - 9)/21/(27 - 7)/63 = 5/21 * 63/20 = 3/4

Which one is correct?

KarishmaB · Answer

Because you don't average out the ratio; you average out the concentration of any one component where the weights used will be volume. Understand that when you find the average of a quantity, it should make physical sense.

Say you know that milk:water = 1:9 in a 100 ml solution. 
When you do 1/9 * 100 ml, what do you get? What is 11.11 ml? Nothing
What you have to do is 1/10 * 100 ml = 10 ml (amount of milk in the solution). 1/10 is the concentration of milk in the solution and you multiply that by the volume of solution.

So here, you have to work with any one component. Say we work with water.
Avg concentration of water = 3/10
Concentration of water in solution 1 = 1/10
Concentration of water in solution 2 = 2/5 = 4/10

w1/w2 = (4/10 - 3/10)/(3/10 - 1/10) = 1/2

P.S. - PM me the link when you want me to reply on a thread. I opened this post by chance. I may not have seen your question directed to me otherwise.

up4gmat · Answer

Hi Bunuel,
I didnt understand the part:
 Question:  \frac{x+9x}{2y+3y}=\frac{2x}{y}=? ?
how did we get this?

Bunuel · Answer

We need to find the ratio of Solution 1 to Solution 2  \frac{solution \ 1}{solution \ 2}=\frac{x+9x}{2y+3y}=\frac{10x}{5y}=\frac{2x}{y}=? , while having that  \frac{x+2y}{9x+3y}=\frac{3}{7} .

Hope it's clear.

bumpbot · Answer

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In what ratio should Solution 1 and Solution 2 be mixed to

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