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In a class, there are 40 boys and their average age is 16 years. One boy, aged 17 years, leaving the class and another joining, the average age becomes 15.875 years. The age of the new boy is :
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- 12 years
- 14.5 years
- 15 years
- 17 years
- 12 years
Correct Option: A
Given that , Age of replaced boy = 17 years
The average age of 40 boys = 16 years.
Total age of 40 boys = 40 × 16 = 640 years
New total age of 40 boys = 40 × 15.875 = 635 years
∴ Age of new boy = [635 – (640 – 17)] = 12 years
Second method to solve this question with the help of given formula :
Here, n = 40 , X = 16 – 15.875 ⇒ X = 0.125
Age of new boy = Age of replaced boy – Xn
Age of new boy = 17 – 0.125 × 40 = 17 – 5
Age of new boy = 12 years
