Question

Ryan was born 6 and one-fourth years after Alexander.The sum of the ages is 66 and eleven-twelfth years.How old is Alexander ?

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{age}\mathrm{of}\mathrm{Ryan}\mathrm{be}\mathrm{x}\mathrm{years} \\ \mathrm{Then}\mathrm{the}\mathrm{age}\mathrm{of}\mathrm{Alexander}\mathrm{will}\mathrm{be}\mathrm{x}+6\frac{1}{4}=\mathrm{x}+\frac{25}{4}\mathrm{years} \\ \mathrm{Also},\mathrm{Sum}\mathrm{of}\mathrm{ages}=66\frac{11}{12} \\ \mathrm{i},\mathrm{e}\mathrm{x}+\mathrm{x}+\frac{25}{4}=\frac{803}{12} \\ \Rightarrow 2\mathrm{x}=\frac{803}{12}-\frac{25}{4} \\ \Rightarrow 2\mathrm{x}=\frac{803-75}{12} \\ \Rightarrow 24\mathrm{x}=728 \\ \Rightarrow \mathrm{x}=\frac{91}{3} \\ \mathrm{So},\mathrm{Alexander}\mathrm{age}=\frac{91}{3}+\frac{25}{4}=\frac{364+75}{12}=\frac{439}{12}=36\frac{7}{12}\mathrm{years} \end{gathered}$$
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