Problems on Ages — “The average age of 30 students is 15 years. Including the teacher, the average becomes 16 years. Find the teacher’s age.”
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A56 years
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B46 years
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C35 years
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D45 years
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E40 years
Answer
Correct Answer: 46 years
Explanation
Introduction / Context:Average problems often require reconstructing the total sum from the average and the number of members. When a new member joins and the average changes, we compare the new total to the old one to isolate the newcomer’s age.
Given Data / Assumptions:
- 30 students have average 15 ⇒ sum_students = 30 * 15.
- With teacher added: members = 31, average = 16 ⇒ new_total = 31 * 16.
- Teacher’s age = new_total − sum_students.
Concept / Approach:Compute both totals explicitly and subtract. This avoids any algebraic confusion and works reliably for all average-with-addition problems.
Step-by-Step Solution:
sum_students = 30 * 15 = 450.new_total = 31 * 16 = 496.Teacher’s age = 496 − 450 = 46 years.Verification / Alternative check:Recalculate average with teacher: (450 + 46)/31 = 496/31 = 16 ✓.
Why Other Options Are Wrong:35/40/45/56 yield totals that do not produce the required 16 average when added to 450 and divided by 31.
Common Pitfalls:Accidentally averaging the two averages; multiplying the teacher’s age by 31; or forgetting that the old total uses 30 while the new total uses 31.
Final Answer:46 years