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 ?

Average age of 10 children = 9 years 9 months
Sum of ages of 10 children = 9 × 10 + $$\frac{9}{12}$$ × 10 = $$\frac{390}{4}$$
Average age of 9 children = 8 years 11 months
Sum of age of 9 children = 8 × 9 + $$\frac{11}{12}$$ × 9 = $$\frac{321}{4}$$
Age of 10th child
= $$\frac{390}{4}$$ - $$\frac{321}{4}$$
= $$\frac{69}{4}$$
= 17 years 3 months