Question

in a school with 10 teachers, one retires and immediately a new teacher of age 25 years joins. as a result, the average age of the teacher reduces by 3. the age of the retired teacher is

Answer 1

To find the age of the retired teacher, an equation was set up using the reduced average age of the school's teachers. Solving this equation showed that the retired teacher was 55 years old.

Step-by-step explanation:

To solve the problem of determining the age of the retired teacher when a new teacher joins a school and reduces the average age by 3, we can set up an equation. Let's assume the original average age of the 10 teachers is A. When one teacher retires and a new 25-year-old teacher joins, the total age of all teachers decreases by 3 years for each of the 10 teachers (a total reduction of 30 years).

The equation to find the original average age A is then: (10A - age of retired teacher + 25) / 10 = A - 3.

Simplify and solve for the age of the retired teacher:

1. 10A - age of retired teacher + 25 = 10 A - 30 (Multiply both sides by 10).
2. Age of retired teacher = 25 + 30
3. Age of retired teacher = 55

Thus, the age of the retired teacher is 55 years.