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Question 69
If a 12 year old boy is replaced by a new boy, then the average age of 18 boys increases by 1.5 years. What is the age of the new boy?
Solution
Let the total sum of 18 boys be A
Let their old average be x years
Given, $$\dfrac{A}{18} = x$$ ==> A = 18x years
Given that 12 year old boy is replaced by a new boy.
Let the age of the new boy by Y years.
Given, $$\dfrac{A-12+Y}{18} = x+1.5$$
=> $$18x-12+Y = 18x+27 => Y = 39$$
Therefore, The age of the new boy = 39 years
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