The average age of 10 children is 9 years 9 months. The average of 9 children is 8 years 11 months. What is the age of the tenth child ?
A. 17 years 3 months B. 18 years 4 months C. 17 years 5 months D. 18 years 3 months Answer: Option AShow Answer
Solution(By Apex Team)
Average age of 10 children = 9 years 9 months
Sum of ages of 10 children
$\begin{array}{l}=9\times 10+\frac{9}{12}\times 10\\
=\Large\frac{390}{4}\end{array}$
Average age of 9 children = 8 years 11 months
Sum of age of 9 children
$\begin{array}{l}=8\times9+\frac{11}{12}\times9\\
=\Large\frac{321}{4}\\
\text{Age of 10th child}\\
=\Large\frac{390}{4}-\frac{321}{4}\\
=\Large\frac{69}{4}\\
\text{= 17 years 3 months}\end{array}$
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