The ratio of ages of two students is 3:2. One is older to the other by 5 years. What is the age of the younger student?

A) 2 years

B) 10 years

C) 15 years

D) None of these

Let’s solve for the younger student’s age:

1. Define variables: Let x represent the age of the younger student.
2. Translate the ratio: The older student’s age can be expressed as 3x (since their age is 3 parts to the younger student’s 2 parts).
3. Translate the age difference: We are given that the older student is 5 years older: 3x = 2x + 5
4. Solve the equation: Combine like terms: x = 5

Therefore, the younger student’s age is B) 10 years (2 * x).