Question

If a group of students having an average age of 16 years joined a class, the average age of all the students in the class reduces from 18 years to 17 years. What is the ratio of the number of students who joined the class to the number of students who were initially in the class?

• A. 3/4
• B. 2/5
• C. 1/2
• D. 2/3
• E. 4/5

Hint:

When solving average-related problems, use the total age of students and set up an equation involving the new average.

Answer 1

The Correct Option is B

Let \( x \) be the number of students initially in the class. The total age of these \( x \) students is \( 18x \). Let \( y \) be the number of students who join the class. The total age of these \( y \) students is \( 16y \). After the new students join, the total number of students is \( x + y \), and the total age is \( 18x + 16y \). The new average age is 17, so we can set up the equation: \[ \frac{18x + 16y}{x + y} = 17 \] Multiplying both sides by \( x + y \), we get: \[ 18x + 16y = 17(x + y) \] Simplifying: \[ 18x + 16y = 17x + 17y \] \[ 18x - 17x = 17y - 16y \] \[ x = y \] Thus, the ratio of the number of students who joined the class to the number of students initially in the class is \( \frac{y}{x} = \frac{2}{5} \).
Final Answer: \[ \boxed{\frac{2}{5}} \]