Question

average lesson i) question​

Answer 1

step by step solution:

9×12+9=117 months

117×10=1170 months

8×12+11=107 months

107×9=963 months

1170-963=207 months

17years 3 months

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Answer 2

$\underline{\textbf{\huge{Question}}}$

The average age of 10 children is 9 year 9 months.The AVERAGe age of 9 children is 8 years 11 months.What is age of Tenth Child?

$\underline{\textbf{\huge{Answer}}}$

$\boxed{\mathtt{Average=\frac{Sum\:of\:all\:terms}{Total\:Terms}}}$

In First Case.

Total Children=10

Average AGE=9 years 9 months.

In Year=$9\frac{9}{12}$years

=$\frac{117}{12}$

Let students Sum of Their ages=x1+x2.........+x10

$\boxed{\mathtt{\frac{x_1+x_2+x_3...+x_{10}}{10}=\frac{117}{12}}}$

$\boxed{\mathtt{x_1+x_2+x_3...+x_{10}=\frac{117}{12}\times10}}$

$\boxed{\mathtt{x_1+x_2+x_3...+x_{10}=\frac{585}{6}}}$

MEANS Sum of 10 students Age=$\frac{585}{6}$years

In Second Case.

Total Student=9

AVERAGe Age=$8\frac{11}{12}$ years.

=$\frac{107}{12}$ years

Let Student and Their Age=x1+x2+x3....+x9

$\boxed{\mathtt{\frac{x_1+x_2+x_3...+x_9}{9}=\frac{107}{12}}}$

$\boxed{\mathtt{x_1+x_2+x_3...+x_9=\frac{107}{12}\times9}}$

$\boxed{\mathtt{x_1+x_2+x_3...+x_9=\frac{321}{4}}}$

Sum of Age of 9 Student=$\frac{321}{4}$ years

Age of 10th Student=$\frac{585}{6}-\frac{321}{4}$

$\frac{207}{12}$

Age =17.25 years

(0.25 is a quater month of
a year=3)

17 years 3 months.

$\boxed{\mathtt{Age\:of\:10th\:Student=17\:years\:3\:months}}$