The ratio of alcohol and water in solutions A and B is 3 : 5 and 5 : 7, respectively. Two litres of A is mixed with 5 litres of B and 3 litres of alcohol is also added to it to get a new solution C. In 1.5 litres of solution C, how much alcohol (in ml) should be mixed so that the ratio of alcohol and water in the final solution becomes 2 : 1?

Correct option is C

Given:

• Solution A: Alcohol : Water = 3 : 5
• Solution B: Alcohol : Water = 5 : 7
• Quantity mixed: 2 litres of A + 5 litres of B + 3 litres alcohol
• From the resulting solution (Solution C), 1.5 litres is taken.
• Additional alcohol is to be added so that the final alcohol : water = 2 : 1
• Find the amount of alcohol (in ml) to be added.

Formula Used:

Component ratio to quantity conversion: 

$$\text{Alcohol} = \left( \frac{\text{Alcohol part}}{\text{Total parts}} \right) \times \text{Total quantity}$$​

​$$\text{Water} = \left( \frac{\text{Water part}}{\text{Total parts}} \right) \times \text{Total quantity}$$​​

Proportional sampling:

$$\text{Sample component} = \left( \frac{\text{Sample size}}{\text{Total solution size}} \right) \times \text{Component amount}$$​​

Ratio condition formula:
​$$\frac{\text{Final alcohol}}{\text{Final water}} = \text{Desired ratio}$$​​

Solution:
Step 1: From solution A (2 litres, ratio 3:5):

Total parts = 3 + 5 = 8

Alcohol = (3/8) × 2 = 0.75 litres

Water = (5/8) × 2 = 1.25 litres

Step 2: From solution B (5 litres, ratio 5:7):

Total parts = 5 + 7 = 12

Alcohol = (5/12) × 5 = 2.083 litres

Water = (7/12) × 5 = 2.917 litres

Step 3: Add 3 litres of alcohol:

Total alcohol = 0.75 + 2.083 + 3 = 5.833 litres

Total water = 1.25 + 2.917 = 4.167 litres

Step 4: In 1.5 litres of solution C (proportionate):

Alcohol = (1.5 / 10) × 5.833 = 0.875 litres

Water = (1.5 / 10) × 4.167 = 0.625 litres

Step 5: Let x litres of alcohol be added to make ratio 2:1:

​$$\frac{0.875 + x}{0.625} = 2 \Rightarrow 0.875 + x = 1.25 \Rightarrow x = 0.375\ \text{litres} = \boxed{375\ \text{ml}}$$​​

Final Answer: 375 ml