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 ?

Options

A. 2 years
B. 10 years
C. `2(1/2)` years
D. 15 years

Answer

To solve the problem, we need to find the age of the younger student given the ratio of their ages and the age difference. Here’s a step-by-step solution:

### Step 1: Define the Variables
Let the ages of the two students be represented as:
- Age of the older student (A) = 3x
- Age of the younger student (B) = 2x

### Step 2: Set Up the Age Difference Equation
According to the problem, the older student is older than the younger student by 5 years. Therefore, we can set up the equation:
\[ 3x - 2x = 5 \]

### Step 3: Simplify the Equation
Now, simplify the equation:
\[ x = 5 \]

### Step 4: Calculate the Ages
Now that we have the value of x, we can find the ages of both students:
- Age of the older student (A) = 3x = 3(5) = 15 years
- Age of the younger student (B) = 2x = 2(5) = 10 years

### Step 5: Conclusion
The age of the younger student is:
\[ \text{Age of the younger student} = 10 \text{ years} \]

### Final Answer
The age of the younger student is **10 years**.

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