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There are two mixtures of honey and water, the quantity of honey in them being 25% and 75% of the mixture respectively. If 2 gallons of the first are mixed with three gallons of the second, what will be the ratio of honey to water in the new mixture?
- a)11: 2
- b)11: 9
- c)9: 11
- d)2: 11
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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There are two mixtures of honey and water, the quantity of honey in th...
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There are two mixtures of honey and water, the quantity of honey in th...
Given:
- Two mixtures of honey and water
- Quantity of honey in the first mixture is 25% of the mixture
- Quantity of honey in the second mixture is 75% of the mixture
- 2 gallons of the first mixture are mixed with 3 gallons of the second mixture
To find:
- Ratio of honey to water in the new mixture
Approach:
1. Calculate the total quantity of honey and water in each mixture
2. Calculate the total quantity of honey and water in the new mixture after combining the two mixtures
3. Find the ratio of honey to water in the new mixture
Calculation:
Let's assume the quantity of honey and water in the first mixture is X and Y gallons respectively.
- Quantity of honey in the first mixture = 25% of X = 0.25X
- Quantity of water in the first mixture = 100% - 25% = 75% of X = 0.75X
Similarly, let's assume the quantity of honey and water in the second mixture is A and B gallons respectively.
- Quantity of honey in the second mixture = 75% of A = 0.75A
- Quantity of water in the second mixture = 100% - 75% = 25% of A = 0.25A
After mixing 2 gallons of the first mixture with 3 gallons of the second mixture, the total quantity of honey in the new mixture is:
0.25X + 0.75A
And the total quantity of water in the new mixture is:
0.75X + 0.25A
The ratio of honey to water in the new mixture can be calculated by dividing the quantity of honey by the quantity of water:
(0.25X + 0.75A) / (0.75X + 0.25A)
Simplifying the above expression:
= (0.25(X + 3A)) / (0.75(X + 3A))
= 0.25 / 0.75
= 1/3
Therefore, the ratio of honey to water in the new mixture is 1:3.
Answer:
The correct ratio of honey to water in the new mixture is 1:3, which is not given in the options. Therefore, the correct answer is None of these.
- Two mixtures of honey and water
- Quantity of honey in the first mixture is 25% of the mixture
- Quantity of honey in the second mixture is 75% of the mixture
- 2 gallons of the first mixture are mixed with 3 gallons of the second mixture
To find:
- Ratio of honey to water in the new mixture
Approach:
1. Calculate the total quantity of honey and water in each mixture
2. Calculate the total quantity of honey and water in the new mixture after combining the two mixtures
3. Find the ratio of honey to water in the new mixture
Calculation:
Let's assume the quantity of honey and water in the first mixture is X and Y gallons respectively.
- Quantity of honey in the first mixture = 25% of X = 0.25X
- Quantity of water in the first mixture = 100% - 25% = 75% of X = 0.75X
Similarly, let's assume the quantity of honey and water in the second mixture is A and B gallons respectively.
- Quantity of honey in the second mixture = 75% of A = 0.75A
- Quantity of water in the second mixture = 100% - 75% = 25% of A = 0.25A
After mixing 2 gallons of the first mixture with 3 gallons of the second mixture, the total quantity of honey in the new mixture is:
0.25X + 0.75A
And the total quantity of water in the new mixture is:
0.75X + 0.25A
The ratio of honey to water in the new mixture can be calculated by dividing the quantity of honey by the quantity of water:
(0.25X + 0.75A) / (0.75X + 0.25A)
Simplifying the above expression:
= (0.25(X + 3A)) / (0.75(X + 3A))
= 0.25 / 0.75
= 1/3
Therefore, the ratio of honey to water in the new mixture is 1:3.
Answer:
The correct ratio of honey to water in the new mixture is 1:3, which is not given in the options. Therefore, the correct answer is None of these.
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