Question

The average age of a group of boys and girls is 18 years. If the average age of boys is 20 years and that of girls is 15 years, then what is the percentage of boys in the group?

• A. 50%
• B. 45%
• C. 60%
• D. 55%

Hint:

To solve problems involving averages, express the relationships between the quantities algebraically and solve the resulting equations.

Answer 1

The Correct Option is C

Step 1: Let the number of boys be \( x \) and the number of girls be \( y \).
The total number of people in the group is \( x + y \), and the average age of the group is 18 years. Thus, the total age is: \[ 20x + 15y = 18(x + y) \] Expanding both sides: \[ 20x + 15y = 18x + 18y \] Simplifying: \[ 2x = 3y \implies x = \frac{3}{2}y \]

Step 2: Find the percentage of boys.
Since \( x = \frac{3}{2}y \), the total number of boys is \( \frac{3}{2}y \), and the total number of people is \( x + y = \frac{3}{2}y + y = \frac{5}{2}y \). Thus, the percentage of boys is: \[ \text{Percentage of boys} = \frac{x}{x + y} \times 100 = \frac{\frac{3}{2}y}{\frac{5}{2}y} \times 100 = \frac{3}{5} \times 100 = 60% \]

Final Answer: \[ \boxed{60%} \]