Question

A mixture contains milk and water in a ratio of 7: 11. When 7 liters of water is added, the ratio changes to 7: 13. Find the quantity of milk in the initial mixture.

• A. 23.5 liters
• B. 24.8 liters
• C. 22.4 liters
• D. 24.5 liters

Hint:

If the milk units were different, you would first multiply the ratios to make the milk parts equal before finding the difference in water.

Answer 1

The Correct Option is D

Concept: When only one component (water) is added, the quantity of the other component (milk) remains unchanged in the ratio.
Step 1: Compare the ratios.
Initial Ratio (M:W) = 7 : 11
Final Ratio (M:W) = 7 : 13
Since the "Milk" part (7) is already the same in both ratios, we can directly compare the "Water" parts.

Step 2: Find the value of one ratio unit.
Increase in Water units = \(13 - 11 = 2 \text{ units}\).
This 2-unit increase is due to adding 7 liters of water.
1 unit = \(7 / 2 = 3.5 \text{ liters}\).

Step 3: Calculate the quantity of milk.
Milk = 7 units = \(7 \times 3.5 = 24.5 \text{ liters}\).