Question

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

Answer 1

Answer:

Average age of 10 children is 9 years 9 months.

12 months together make one year.

→ Age of 10 children = \sf{9\:+\:\dfrac{9}{12}}9+129

Age of 1 children = \sf{9(10)\:+\:\dfrac{9}{12}(10)}9(10)+129(10)

\rightarrow\:\sf{90\:+\:\dfrac{90}{12}}→90+1290

\rightarrow\:\sf{\dfrac{1080\:+\:90}{12}}→121080+90

\rightarrow\:\sf{\dfrac{1170}{12}}→121170

\rightarrow\:\sf{\dfrac{390}{4}}→4390 ...(1)

Similarly,

Average age of 9 children is 8 years 11 months.

→ Age 9 children = \sf{8\:+\:\dfrac{11}{12}}8+1211

Age of 1 children = \sf{8(9)\:+\:\dfrac{9}{12}(9)}8(9)+129(9)

\rightarrow\:\sf{72\:+\:\dfrac{81}{12}}→72+1281

\rightarrow\:\sf{\dfrac{864\:+\:81}{12}}→12864+81

\rightarrow\:\sf{\dfrac{945}{12}}→12945

\rightarrow\:\sf{\dfrac{321}{4}}→4321 ....(2)

Now, we have to find the age of tenth child.

So,

Age of tenth child = Average age of 10 children - Average age of 9 children

Substitute value of equation (1) and (2) above, to find the age of tenth child

\implies\:\sf{\dfrac{390}{4}\:-\:\dfrac{321}{4}}⟹4390−4321

\implies\:\sf{\dfrac{390\:-\:321}{4}}⟹4390−321

\implies\:\sf{\dfrac{69}{4}}⟹469

\implies\:\sf{17.25}⟹17.25