Question

The ratio of the ages of four members in the family is 13:14:49:65.the average age is 141.what is the ratio.

Answer 1

$\mathsf{Let, \ the \ \ ages \ \ be \ \ 13a, \ \ 14a, \ \ 49a \ \ and}$
$\sf{65a.}$



$\sf{Total \ \ number \ \ of \ \ ages \ \ = \ \ 4}$



$\mathsf{Sum \ \ of \ \ all \ \ these \ \ ages \ \ = \ 13a \ + \ 14a \ +}$
$\sf{49a \ + \ 65a \ = \ 141a}$



$\sf{Average \ \ age \ = \ 141}$ $\sf{ \qquad \qquad ( \ Given \ )}$



$\sf{Now,}$



${\boxed{\boxed{\sf{\red{Average \ = \ {\dfrac{Sum \ \ of \ \ all \ \ ages}{Total \ \ no. \ \ of \ \ ages}}}}}}}$



$\sf{141 \ = \ {\dfrac{141a}{4}}}$



$\sf{{\cancel{141}} \ = \ {\dfrac{{\cancel{141}}a}{4}}}$



$\sf{1 \ = \ {\dfrac{a}{4}}}$



$\sf{a \ = \ 4}$



$\sf{Ages \ :}$



$\sf{13a \ = \ 13 × 4 \ =}$ $\bold{52 \ years}$



$\sf{14a \ = \ 14 × 4 \ =}$ $\bold{56 \ years}$



$\sf{49a \ = \ 49 × 4 \ =}$ $\bold{196 \ years}$



$\sf{65a \ = \ 65 × 4 \ =}$ $\bold{260 \ years}$