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Equal quantities of two mixtures containing chocolate milk and water in the ratio of 1:2 and 2:3 were mixed to form mixture A. Equal quantities of two other mixtures containing almond milk and water in the ratio of 3:4 and 4:5 were mixed to form a mixture S. If mixtures A and S were mixed in a ratio of 6:7, find the ratio of quantities of chocolate milk and almond milk in the resultant mixture.
A. 18:25
B. 18:23
C. 19:24
D. 21:30
E. 2:3
A. 18:25
B. 18:23
C. 19:24
D. 21:30
E. 2:3
10 Jul 2024, 00:00
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Step 1: Find the ratio of chocolate milk to water in mixture A.
Mixture 1: 1 part chocolate milk, 2 parts water
Mixture 2: 2 parts chocolate milk, 3 parts water
Since equal quantities are mixed, we can average the ratios: (1+2)/2 : (2+3)/2 = 3:5
So, mixture A has 3 parts chocolate milk and 5 parts water.
Step 2: Find the ratio of almond milk to water in mixture S.
Mixture 3: 3 parts almond milk, 4 parts water
Mixture 4: 4 parts almond milk, 5 parts water
Average the ratios: (3+4)/2 : (4+5)/2 = 7:9
So, mixture S has 7 parts almond milk and 9 parts water.
Step 3: Consider the mixing of A and S.
Mixture A (chocolate milk and water) is mixed with mixture S (almond milk and water) in the ratio 6:7.
This means the proportion of chocolate milk in the final mixture is: (6/13) * (3/8) = 9/52
The proportion of almond milk in the final mixture is: (7/13) * (7/16) = 49/208
Step 4: Find the ratio of chocolate milk to almond milk.
To find the ratio, we need to get rid of the denominators:
Multiply the proportion of chocolate milk by 4/4: (9/52) * 4/4 = 36/208
Multiply the proportion of almond milk by 1: (49/208) * 1 = 49/208
Step 5: Simplify the ratio.
The ratio of chocolate milk to almond milk is 36/208 : 49/208
Simplfying the ratio we get 18:25 (approx)
Mixture 1: 1 part chocolate milk, 2 parts water
Mixture 2: 2 parts chocolate milk, 3 parts water
Since equal quantities are mixed, we can average the ratios: (1+2)/2 : (2+3)/2 = 3:5
So, mixture A has 3 parts chocolate milk and 5 parts water.
Step 2: Find the ratio of almond milk to water in mixture S.
Mixture 3: 3 parts almond milk, 4 parts water
Mixture 4: 4 parts almond milk, 5 parts water
Average the ratios: (3+4)/2 : (4+5)/2 = 7:9
So, mixture S has 7 parts almond milk and 9 parts water.
Step 3: Consider the mixing of A and S.
Mixture A (chocolate milk and water) is mixed with mixture S (almond milk and water) in the ratio 6:7.
This means the proportion of chocolate milk in the final mixture is: (6/13) * (3/8) = 9/52
The proportion of almond milk in the final mixture is: (7/13) * (7/16) = 49/208
Step 4: Find the ratio of chocolate milk to almond milk.
To find the ratio, we need to get rid of the denominators:
Multiply the proportion of chocolate milk by 4/4: (9/52) * 4/4 = 36/208
Multiply the proportion of almond milk by 1: (49/208) * 1 = 49/208
Step 5: Simplify the ratio.
The ratio of chocolate milk to almond milk is 36/208 : 49/208
Simplfying the ratio we get 18:25 (approx)
10 Jul 2024, 01:12
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I used example numbers to solve this.
- Mix 1 -> 1:2. 1/3, 2/3 are the proportions. Mix 2 -> 2:3. 2/5, 3/5 are the proportions. Took lcm(3,5) = 15 as the equal quantity of mix 1 and mix 2 used to arrive at mix A.
- In a similar fashion, took 63 as the equal quantity of the 2 mixtures used to get mix B.
- Converted the final numbers of mix A:mix B to 6:7 as shown.
___
Harsha
Enthu about all things GMAT | Exploring the GMAT space | My website: gmatanchor.com
GMAT-Club-Forum-qurv86mw.png [ 140.44 KiB | Viewed 1450 times ]
- Mix 1 -> 1:2. 1/3, 2/3 are the proportions. Mix 2 -> 2:3. 2/5, 3/5 are the proportions. Took lcm(3,5) = 15 as the equal quantity of mix 1 and mix 2 used to arrive at mix A.
- In a similar fashion, took 63 as the equal quantity of the 2 mixtures used to get mix B.
- Converted the final numbers of mix A:mix B to 6:7 as shown.
___
Harsha
Enthu about all things GMAT | Exploring the GMAT space | My website: gmatanchor.com
Attachment:
GMAT-Club-Forum-qurv86mw.png [ 140.44 KiB | Viewed 1450 times ]
