Vipin adds 3 litres of liquid A in 6 litres of liquid B and Mohit adds 8 litres of liquid A in 15 litres of liquid B. What is the ratio of the percentage of liquid B in the two mixtures?

Options

A. `26:25`
B. `51:32`
C. `46:45`
D. `34:25`

Answer

To solve the problem, we need to find the percentage of liquid B in the mixtures prepared by Vipin and Mohit, and then determine the ratio of these percentages.

### Step-by-Step Solution:

1. **Calculate the total volume of the mixture for Vipin:**
- Vipin adds 3 liters of liquid A and 6 liters of liquid B.
- Total volume = Volume of A + Volume of B = 3 liters + 6 liters = 9 liters.

2. **Calculate the percentage of liquid B in Vipin's mixture:**
- Percentage of B = (Volume of B / Total volume) × 100
- Percentage of B = (6 liters / 9 liters) × 100 = (6/9) × 100 = 66.67%.

3. **Calculate the total volume of the mixture for Mohit:**
- Mohit adds 8 liters of liquid A and 15 liters of liquid B.
- Total volume = Volume of A + Volume of B = 8 liters + 15 liters = 23 liters.

4. **Calculate the percentage of liquid B in Mohit's mixture:**
- Percentage of B = (Volume of B / Total volume) × 100
- Percentage of B = (15 liters / 23 liters) × 100 = (15/23) × 100 ≈ 65.22%.

5. **Find the ratio of the percentages of liquid B in the two mixtures:**
- Ratio = Percentage of B in Vipin's mixture : Percentage of B in Mohit's mixture
- Ratio = 66.67 : 65.22.

6. **Convert the percentages to a simpler ratio:**
- To simplify, we can express both percentages as fractions:
- Ratio = (66.67 / 65.22) = (2000 / 1957) (after multiplying both by 100).
- This can be simplified further if needed, but for practical purposes, we can use these values directly.

### Final Answer:
The ratio of the percentage of liquid B in the two mixtures is approximately **66.67 : 65.22**.