The ratio of present ages of Ranjini and Shahid is 5:4. After 13 years the ratio of their ages will be 6:5. What is Ranjini's present age?

Let the present age of Ranjini be 5x and Shahid be 4x.
After 13 years, their ages will be 5x+13 and 4x+13 respectively.

Given the new ratio:

4x+13
5x+13
​
=
5
6
​

Cross-multiplying to solve for x:

5(5x+13)=6(4x+13)
25x+65=24x+78
25x−24x=78−65
x=13
Ranjini's present age:

5x=5×13=65 years