Two Solutions Having Milk and Water in the Ratios 3 : 5 and 4 : 7 are GMAT Problem Solving

Question: Two solutions having milk and water in the ratios 3 : 5 and 4 : 7 are mixed in the ratio 2 : 3. What is the ratio of milk and water in the resultant mixture?

  1. 80 : 139
  2. 81 : 139
  3. 82 : 139
  4. 83 : 139
  5. 84 : 139

Correct Answer: B

Solution and Explanation:
Approach Solution 1:

Given to us in the question that two solutions having milk and water in the ratios 3 : 5 and 4 : 7 are mixed in the ratio 2 : 3.
It has asked to find the ratio of milk and water in the final mixture.
It is given that there are two solutions.

Let the solutions be sol1 and sol2.
Let there be a 1L solution of each type.
In sol1, the amount of milk will be 3/8L
In sol2, the amount of milk will be 4/11L
Let the amount of milk in the final solution be x
These solutions are mixed in the ratio of 2:3

We get,
(x - 4/11) / (⅜-x) = ⅔
3x -12/11 = ¾ - 2x
Taking 2x to left side and constant term to right,
3x + 2x = ¾ + 12/11
5x = (33+48)/44
5x = 81/44
X = 81/220
This is the ratio of milk in the total mixture.
Subtracting by 1, we’ll get the ratio of water in total mixture.
Let w be ratio of water in total mixture.
W = 1-x
    = 1 - 81/220
    = 139 / 220

This the ratio of water in the total mixture.
Now it has asked the question to find out the ratio of milk to water in final mixture.

The ratio of milk : water = 81/220 / 139/220
                                      = 81/139

Approach Solution 2:
Given to us in the question that two solutions having milk and water in the ratios 3 : 5 and 4 : 7 are mixed in the ratio 2 : 3
Let the given ratios be
3:5 = 8x
4:7 = 11x
Lcm of 11 and 8 is 88.
SO multiply 11 at the top equation ans 8 at the bottom we get,
33:55 = 88x
32:56 = 88x

Now they are mixed in the ratio of 2:3
33*2 + 32*3 : 55*2 + 56*3 = 162 : 278
This can be reduced to 81:139

Approach Solution 3:
First, [m:w] = [ 3 : 5 ] ; sum=8
Second, [m:w]=[ 4 : 7 ] ; sum =11
mixture [m:w]=[ 2 : 3 ]

LCM of first and second is (8,11)= 88
Now, back to first
[m:w]= [3 : 5]*[88/8]
=[3 : 5]*11
=[33:55]

Back to second,
[m:w]=[4:7]*[88/11]
= [32:56]

Now, multiplying first and second corresponding to mixture,we get,

[m:w]=[33:55]*2
=[66:110]

& [m:w]=[32:56]*3
=[96:168]

Now ,combine this two milk and water, we get,
[M:W]=[66+96:110+168]
=[162:278]
=[81:139]

Two solutions having milk and water in the ratios 3 : 5 and 4 : 7 are”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.


 

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