Question

The average age of 100 teachers in a college in 2000 was 50 years. In 2002, 20 teachers superannuated from their jobs, whose average age was 60 years. In 2005, 40 new teachers joined the college whose average age was 38 years. What was the average age of all the teachers in 2008?

• A. 54 years
• B. 49 years
• C. 51 years
• D. 50 years

Hint:

In average age problems, always convert averages into total ages first. Then adjust totals whenever people leave, join, or grow older.

Answer 1

The Correct Option is C

Step 1: In 2000 the average age is 50 for 100 teachers. By 2002, each person is simply 2 years older, so the average becomes \( 50+2=52 \), still for 100 teachers.

Step 2: When the 20 teachers averaging 60 years retire, the new average of the remaining 80 is a weighted average: \( \frac{100 \times 52 - 20 \times 60}{80} = \frac{5200-1200}{80} = 50 \).

Step 3: By 2005, 3 more years pass, so this group's average becomes \( 50+3=53 \). Merging in the 40 new teachers averaging 38 gives a combined average for all 120: \( \frac{80 \times 53 + 40 \times 38}{120} = \frac{4240+1520}{120} = \frac{5760}{120}=48 \).

Step 4: By 2008, 3 more years pass for everyone, so the final average is \( 48+3=51 \).
\[ \boxed{51 \text{ years}} \]