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The ratios of alcohol to water in solutions A and B are 3 ∶ 5 and 9 ∶ 7, respectively. A and B are mixed in the ratio 5 ∶ 8. In 520 ml of the resulting solution, how much water (in ml) should be mixed so as to obtain a solution in which the ratio of alcohol to water is 3 ∶ 4?
- a)85
- b)75
- c)80
- d)90
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The ratios of alcohol to water in solutions A and B are 3 ∶ 5 and 9 ∶...
Given:
Ratio of alcohol to water in solution A = 3 : 5
Ratio of alcohol to water in solution B = 9 : 7
Ratio of A and B mixed = 5 : 8
Volume of resulting solution = 520 ml
To find:
How much water (in ml) should be mixed to obtain a solution with alcohol to water ratio of 3 : 4
Solution:
Let the volume of solution A be 3x and the volume of solution B be 9y.
According to the given ratios, the volume of alcohol and water in solution A are:
Volume of alcohol in A = 3/8 * 3x = 9x/8
Volume of water in A = 5/8 * 3x = 15x/8
Similarly, the volume of alcohol and water in solution B are:
Volume of alcohol in B = 9/16 * 9y = 81y/16
Volume of water in B = 7/16 * 9y = 63y/16
When A and B are mixed in the ratio 5 : 8, the total volume of the resulting solution is:
3x + 9y = 520
Simplifying this equation, we get:
x + 3y = 173.33
Now, let's find the volume of alcohol and water in the resulting mixture:
Volume of alcohol = 3/8 * 520 = 195 ml
Volume of water = 5/8 * 520 = 325 ml
Let's assume that we need to add x ml of water to the resulting mixture to obtain the required alcohol to water ratio of 3 : 4.
So, the new volume of water in the mixture will be:
325 + x
And the new volume of alcohol will remain the same, i.e. 195 ml.
According to the given ratio, the new volume of water should be 4/7 times the volume of alcohol:
(325 + x)/(195) = 4/7
Simplifying this equation, we get:
x = 75 ml
Therefore, we need to add 75 ml of water to the resulting mixture to obtain the required alcohol to water ratio of 3 : 4.
Hence, the correct answer is option B.
Ratio of alcohol to water in solution A = 3 : 5
Ratio of alcohol to water in solution B = 9 : 7
Ratio of A and B mixed = 5 : 8
Volume of resulting solution = 520 ml
To find:
How much water (in ml) should be mixed to obtain a solution with alcohol to water ratio of 3 : 4
Solution:
Let the volume of solution A be 3x and the volume of solution B be 9y.
According to the given ratios, the volume of alcohol and water in solution A are:
Volume of alcohol in A = 3/8 * 3x = 9x/8
Volume of water in A = 5/8 * 3x = 15x/8
Similarly, the volume of alcohol and water in solution B are:
Volume of alcohol in B = 9/16 * 9y = 81y/16
Volume of water in B = 7/16 * 9y = 63y/16
When A and B are mixed in the ratio 5 : 8, the total volume of the resulting solution is:
3x + 9y = 520
Simplifying this equation, we get:
x + 3y = 173.33
Now, let's find the volume of alcohol and water in the resulting mixture:
Volume of alcohol = 3/8 * 520 = 195 ml
Volume of water = 5/8 * 520 = 325 ml
Let's assume that we need to add x ml of water to the resulting mixture to obtain the required alcohol to water ratio of 3 : 4.
So, the new volume of water in the mixture will be:
325 + x
And the new volume of alcohol will remain the same, i.e. 195 ml.
According to the given ratio, the new volume of water should be 4/7 times the volume of alcohol:
(325 + x)/(195) = 4/7
Simplifying this equation, we get:
x = 75 ml
Therefore, we need to add 75 ml of water to the resulting mixture to obtain the required alcohol to water ratio of 3 : 4.
Hence, the correct answer is option B.
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Community Answer
The ratios of alcohol to water in solutions A and B are 3 ∶ 5 and 9 ∶...
Given:
The ratios of alcohol to water in solutions A and B are 3 ∶ 5 and 9 ∶ 7, respectively.
A and B are mixed in the ratio 5 ∶ 8.
Calculation:
In 520 ml of the new solution:
Solution A = 520 × 5/13
⇒ 200 ml
Solution B = 520 × 8/13
⇒ 320 ml
Now,
Portion of alcohol in solution A = 200 ml × 3/8
⇒ 75 ml
Portion of alcohol in solution B = 320 ml × 9/16
⇒ 180 ml
Total alcohol = 75 + 180
⇒ 255 ml
Portion of water in solution A = 200 ml × 5/8
⇒ 125 ml
Portion of water in solution B = 320 ml × 7/16
⇒ 140 ml
Total water = 125 + 140
⇒ 265 ml
Now,
In the new solution amount of alcohol will be same,
So, new amount of water = 255 × 4/3
⇒ 340 ml
Extra water = 340 - 265
⇒ 75 ml
∴ Required answer is 75 ml.
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The ratios of alcohol to water in solutions A and B are 3 ∶ 5 and 9 ∶ 7, respectively. A and B are mixed in the ratio 5 ∶ 8. In 520 ml of the resulting solution, how much water (in ml) should be mixed so as to obtain a solution in which the ratio of alcohol to water is 3 ∶ 4?a)85b)75c)80d)90Correct answer is option 'B'. Can you explain this answer?
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