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

$\bold{given : } \\ \\ average \: age \: of \: 10 \: children \: is \: 9 \: yrs \\ \: 9 \: months \\ \\ \\ \\ \bold {9 \: yrs \: 9 \: months} \\ \\ 9 \times 12 + 9 \: months \\ \\ 108 + 9 months \\ \\ \bold{118 \:months} \\ \\ \\ \\ \: \bold{sum \: of \:ages \: of \: 10 \: children :} \\ \\ \bold {mean \: age\: \times \: no. \: of \: children} \\ \\ 10 \times 118 \\ \\ \bold{1180 \: months}$
$average \: age \: of \: 9 \: children : \\ \\ 8 \: yrs \: 11 \: months \\ \\ \\ \\\bold{ 8 \: yrs \: 11 \: months} \: \\ \\ 8 \times 12 + 11 \: months \\ \\ 96 + 11 \: months \\ \\\bold{ 107 months }\: \\ \\ \\ \\ \bold{sum \: of \: ages \: of \: 9 \: children : }\\ \\ \bold{mean \: age \: \times \: no. \: of \: children :} \\ \\ 107 \times 9 \\ \\ \bold{963 \: months}$
$sum \: of \: ages \: of \: 10 \: children \: \\ - \\ sum \: of \: ages \: of \: 9 \: children \\ - - - - - - - - - - - - - \\ \bold{age \: of \: 10th \: child} \\ \\ \\ \\ 1180 \\ - \\ 963 \\ - - - - \\ \bold{217 \: months }\\ \\ \\ \\ \bold{217 \: months :} \\ \\ \frac{217}{12} \\ \\ \bold{18 \: yrs \: 1 \: month }\:$$\bold {age \:of\: 10th\: child : } \\ \\ \bold {18 \:yrs\: and \:1\: month}$