Let's solve the problem step by step.

Step 1: Understanding the given information

• The age ratio of A to B is 4:9.
• B's age is double of A's age.

Step 2: Express the ages of A and B in terms of variables

Let the age of A be $4x$ years and the age of B be $9x$ years, where $x$ is a common multiplier.

Step 3: Use the information that B's age is double of A's age

According to the problem, B's age is twice A's age. So, we can set up the equation:

$9x = 2(4x)$

Simplifying the equation:

$9x = 8x$

This equation is not true unless $x = 0$, which is impossible since age cannot be zero. This indicates that there is some inconsistency in the given problem. Let's analyze the information further:

If B's age is double A's age, the correct ratio should be 1:2. However, given the ratio 4:9, B's age cannot be exactly double A's age. This discrepancy means the problem might be misstated.

Step 4: Difference in percentage using the given ratio

Ignoring the incorrect "double" condition, we can still calculate the difference in their ages in percentage using the ratio 4:9.

The difference between the ages is:

$\text{Difference} = 9x - 4x = 5x$

To find the percentage difference relative to A's age:

$\text{Percentage Difference} = \left(\frac{5x}{4x}\right) \times 100\% = \left(\frac{5}{4}\right) \times 100\% = 125\%$

Thus, the difference in ages between A and B is 125% of A's age.

Conclusion:

The difference between the ages of A and B, considering the given ratio of 4:9, is 125% of A's age. However, note that this calculation is based solely on the ratio, not on the condition that B's age is twice A's age, which is contradictory.

Would you like more details or have any questions?

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Here are 5 related questions:

1. How can we check if a ratio correctly represents the relationship between two quantities?
2. What would happen if the ratio was 1:2 instead of 4:9?
3. How do we convert a ratio into percentage form?
4. Can a ratio be simplified further when given more information?
5. How do age-related word problems help in understanding ratios and proportions?

Tip: When solving ratio problems, ensure the given conditions are consistent before proceeding with calculations.