Question

the average age of 10 children is 9 yrs 9 mths . the average age of 9 children is 8 yrs 11 mths. what is the age of the tenth child​

Answer 1

Average age of 10 children is 9 years 9 months.

12 months together make one year.

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

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

$\rightarrow\:\sf{90\:+\:\dfrac{90}{12}}$

$\rightarrow\:\sf{\dfrac{1080\:+\:90}{12}}$

$\rightarrow\:\sf{\dfrac{1170}{12}}$

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

Similarly,

Average age of 9 children is 8 years 11 months.

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

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

$\rightarrow\:\sf{72\:+\:\dfrac{81}{12}}$

$\rightarrow\:\sf{\dfrac{864\:+\:81}{12}}$

$\rightarrow\:\sf{\dfrac{945}{12}}$

$\rightarrow\:\sf{\dfrac{321}{4}}$ ....(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

$\implies\:\sf{\dfrac{390}{4}\:-\:\dfrac{321}{4}}$

$\implies\:\sf{\dfrac{390\:-\:321}{4}}$

$\implies\:\sf{\dfrac{69}{4}}$

$\implies\:\sf{17.25}$

•°• Age of tenth child is 17 years 3 months.

Answer 2

$\LARGE\underline{\underline{\sf Given:}}$

• Average age of 10 children is =9years 9 months

• Average age of 9 children is = 8years 11 months

$\LARGE\underline{\underline{\sf To\:Find:}}$

• Age of the tenth child = ?

$\LARGE\underline{\underline{\sf Solution:}}$

Sum of Ages of 10 children :

$\large\implies{\sf 9×10+\dfrac{9}{12}×10 }$

$\large\implies{\sf \dfrac{390}{4}}$

$\large\implies{\sf 97.5 }$

Sum of Ages of 9 children :

$\large\implies{\sf 8×9+\dfrac{11}{12}×9 }$

$\large\implies{\sf \dfrac{321}{4}}$

$\large\implies{\sf 80.25}$

Now ,

Age of 10th Child :

$\large\implies{\sf 97.5-80.25 }$

$\large\implies{\sf 17.25\:years }$

Or

$\large\implies{\sf 17\:years\:3\:months}$

________________________________________

$\LARGE\underline{\underline{\sf Answer:}}$

•°• Age of 10th child is 17 years 3 months.