There are two mixtures of honey and water, the quantity of honey in them being 25% and 75% of the mixture. 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?

Options

A. `11:2`
B. `11:9`
C. `9:11`
D. `2:11`

Answer

To solve the problem, we need to find the ratio of honey to water in the new mixture created by combining two different mixtures of honey and water.

### Step-by-Step Solution:

1. **Identify the Mixtures**:
- The first mixture has 25% honey and 75% water.
- The second mixture has 75% honey and 25% water.

2. **Convert Percentages to Fractions**:
- 25% can be expressed as \( \frac{1}{4} \) (honey) and \( \frac{3}{4} \) (water) for the first mixture.
- 75% can be expressed as \( \frac{3}{4} \) (honey) and \( \frac{1}{4} \) (water) for the second mixture.

3. **Calculate the Amounts in Each Mixture**:
- For the first mixture (2 gallons):
- Honey = \( 25\% \) of 2 gallons = \( 0.25 \times 2 = 0.5 \) gallons
- Water = \( 75\% \) of 2 gallons = \( 0.75 \times 2 = 1.5 \) gallons
- For the second mixture (3 gallons):
- Honey = \( 75\% \) of 3 gallons = \( 0.75 \times 3 = 2.25 \) gallons
- Water = \( 25\% \) of 3 gallons = \( 0.25 \times 3 = 0.75 \) gallons

4. **Combine the Amounts**:
- Total Honey = Honey from first mixture + Honey from second mixture
- Total Honey = \( 0.5 + 2.25 = 2.75 \) gallons
- Total Water = Water from first mixture + Water from second mixture
- Total Water = \( 1.5 + 0.75 = 2.25 \) gallons

5. **Calculate the Ratio of Honey to Water**:
- Ratio of Honey to Water = Total Honey : Total Water
- Ratio = \( 2.75 : 2.25 \)

6. **Simplify the Ratio**:
- To simplify, we can divide both sides by 0.25:
- \( \frac{2.75}{0.25} : \frac{2.25}{0.25} = 11 : 9 \)

### Final Answer:
The ratio of honey to water in the new mixture is **11:9**.

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