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Problem 1: The ages of A and B are in the ratio 4:5. Four years ago, the ratio of their ages was 7:9. Find their present ages.

Solution:

Let the present ages of A and B be $4x$ and $5x$ respectively.

According to the problem:

• Four years ago, the ratio of their ages was 7:9.

So, four years ago:

• Age of A was $4x - 4$.
• Age of B was $5x - 4$.

The ratio of their ages four years ago is given by: $\frac{4x - 4}{5x - 4} = \frac{7}{9}$

Cross-multiplying to eliminate the fraction: $9(4x - 4) = 7(5x - 4)$ $36x - 36 = 35x - 28$

Now, solving for $x$: $36x - 35x = 36 - 28$ $x = 8$

So, the present ages of A and B are:

• A's age = $4x = 4(8) = 32$ years
• B's age = $5x = 5(8) = 40$ years

Answer: The present ages of A and B are 32 years and 40 years, respectively.

Would you like a detailed explanation, or do you have any other questions? Here are five related problems you might find useful:

1. If the ratio of the ages of C and D is 3:4, and after 5 years the ratio becomes 4:5, find their present ages.
2. The ages of two people are in the ratio 7:8. Eight years ago, their ages were in the ratio 5:6. Find their current ages.
3. A father is three times as old as his son. In 15 years, he will be twice as old as his son. What are their current ages?
4. If the sum of the ages of A and B is 50 years, and 5 years ago, the ratio of their ages was 2:3, what are their current ages?
5. The ages of two friends are in the ratio 5:6. Ten years ago, the ratio was 4:5. Find their current ages.

Tip: When working with age-related word problems, setting up the correct equations based on the given ratios and then solving for the unknowns step by step is crucial for accuracy.