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Let's analyze the question:

**Given:**
- A 420 liters mixture of milk and water.
- The ratio of milk to water is 5:2.
- We need to add some water so that the percentage of milk in the mixture becomes 62.5%.

**Solution:**

1. **Current quantity of milk and water:**

   - The ratio of milk to water is 5:2, so the total ratio parts = \(5 + 2 = 7\).

   - Quantity of milk = \(\frac{5}{7} \times 420 = 300\) liters.

   - Quantity of water = \(\frac{2}{7} \times 420 = 120\) liters.

2. **New percentage of milk in the mixture:**

   - Let \(x\) be the amount of water to be added.

   - Total amount of mixture after adding water = \(420 + x\) liters.

   - New percentage of milk = \(\frac{300}{420 + x} \times 100 = 62.5\%\).

3. **Set up the equation:**

   \[
   \frac{300}{420 + x} \times 100 = 62.5
   \]

   Simplify:

   \[
   \frac{300}{420 + x} = 0.625
   \]

   \[
   300 = 0.625 \times (420 + x)
   \]

   \[
   300 = 262.5 + 0.625x
   \]

   \[
   300 - 262.5 = 0.625x
   \]

   \[
   37.5 = 0.625x
   \]

   \[
   x = \frac{37.5}{0.625} = 60
   \]

So, **60 liters** of water should be added to the mixture.

**Answer: 60 liters (Option C).**

Would you like further clarification or details? 

### Related Questions:
1. What is the current percentage of milk in the original mixture?
2. How do you calculate the ratio of milk to water after adding 60 liters of water?
3. If 80 liters of water were added, what would be the new percentage of milk?
4. How to find the initial amount of milk if the mixture ratio changes?
5. What would happen if instead of water, 60 liters of milk were added?

**Tip:** Always double-check the total quantities in mixture problems to ensure you are correctly calculating percentages and proportions.

In a 420 liters mixture of milk and water, the ratio of the milk to water is 5:2. How much quantity of water should be added in the mixture so that the percentage of the milk in the mixture becomes 62.5%?

Explore how to adjust the water content in a milk-water mixture to achieve a specific percentage of milk. The problem involves understanding ratios, percentages, and algebraic calculation to determine the required amount of water addition.

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