The question asks about the present age of Anitha, where the present age of Anitha and Anjali is in the ratio 3:4. It also states that 5 years ago, their ages were in the ratio 2:3. We are required to find the present age of Anitha.

Step-by-step Solution:

1. Let the present age of Anitha be $3x$ and the present age of Anjali be $4x$, since their ages are in the ratio 3:4.

2. Five years ago, Anitha’s age was $3x - 5$, and Anjali’s age was $4x - 5$.

3. According to the problem, the ratio of their ages 5 years ago was 2:3, so we can set up the equation: $\frac{3x - 5}{4x - 5} = \frac{2}{3}$

4. Cross-multiply to eliminate the fractions: $3(3x - 5) = 2(4x - 5)$ Expanding both sides: $9x - 15 = 8x - 10$

5. Solve for $x$: $9x - 8x = -10 + 15$ $x = 5$

6. Now that we know $x = 5$, we can find Anitha’s present age: $\text{Anitha's age} = 3x = 3(5) = 15$

Conclusion:

The present age of Anitha is 15 years.

Would you like any further details or clarifications?

Here are five related questions you can explore:

1. What is Anjali's current age?
2. How would the solution change if the ratio 5 years ago was different?
3. Can this problem be solved graphically?
4. How does this method generalize to other age-related problems?
5. What if Anitha’s age were given explicitly, and you had to find Anjali’s?

Tip: In word problems involving ratios and ages, setting variables and forming equations based on the given relationships is a key strategy to solve them efficiently.