Question

The average age of 10 children is 9 year 9 months. The average age of 9 children is 8 year 11 months.What is the age of the tenth child? ​

Answer 1

Answer:

$\huge\blue{\boxed{\sf AnSwEr}}$

Average age of 10 children = 9 years 9 months

sum of ages of 10 children =

$→9 \times 10 + \frac{9}{12} \times 10$

$\green{\boxed{\sf → \frac{390}{4} }}$

Average age of 9 children = 8 years 11 months

sum of age of 9 children =

$→ 8 \times 9 + 9 \times \frac{11}{12}$

$\green{\boxed{\sf → \frac{321}{4} }}$

Age of 10th child

$→ \frac{390}{4} - \frac{321}{4}$

$→ \frac{390 - 321}{4}$

$→ \frac{69}{4}$

$\huge\red{\boxed{\sf → 17years\:3months }}$