In a class, there are 20 boys whose average age is decreased by 2 months, when…
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In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 18 years is replaced by a new boy. The age of the new boy is :
- A.
14 years 8 months
- B.
15 years
- C.
16 years 4 months
- D.
17 years 10 months
Attempted by 22 students.
Show answer & explanation
Correct answer: A
Solution: 1
Let average age of the class was A months initially.
Total age of all students combined initially = 20 × A
Let the age of newly added boy is B months.
New average age of the class = (A – 2) months [Average decreased by 2 months]
New total age of all students combined = 20 × (A – 2) months.
∴ 20 × (A – 2) = (20 × A) – (18 × 12) + B [18 year boy replaced by B]
⇒ – 40 = B – (216)
⇒ B = 216 – 40 = 176 months = 14 years and 8 months
Note: All ages are used in months for convenience.