Five years ago, the difference between the ages of Rajesh and Rahul was 2 years. After 10 years from now, the ratio of their ages will be 15 : 16. Find the ratio of their ages after 4 years from now.

Let the present ages of Rajesh and Rahul be x and y. The difference in their ages is constant, so y minus x equals 2. After 10 years, the ratio x plus 10 over y plus 10 equals 15 over 16, which gives 16x plus 160 equals 15y plus 150, or 16x minus 15y equals negative 10. Substituting y equals x plus 2 gives 16x minus 15x minus 30 equals negative 10, so x equals 20 and y equals 22. The ratio of their ages after 4 years is 24 to 26, which simplifies to 12 to 13.

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