# The difference between the present ages of Tara and her father is 24 years. Five years ago, she was one-fifth her father's age. Find their present ages.

Please find below the solution to the asked query :

$\mathrm{Let}\mathrm{the}\mathrm{ages}\mathrm{of}\mathrm{Mira}\mathrm{and}\mathrm{fathers}\mathrm{are}\mathrm{y}\mathrm{and}\mathrm{x}\phantom{\rule{0ex}{0ex}}\mathrm{x}-\mathrm{y}=24.....\left(1\right)\phantom{\rule{0ex}{0ex}}\mathrm{now}\mathrm{ages}\mathrm{five}\mathrm{years}\mathrm{ago}\mathrm{was}\phantom{\rule{0ex}{0ex}}\mathrm{x}-5,\mathrm{y}-5\phantom{\rule{0ex}{0ex}}\mathrm{Now}\mathrm{according}\mathrm{to}\mathrm{the}\mathrm{question},\phantom{\rule{0ex}{0ex}}\mathrm{y}-5=\frac{1}{5}\left(\mathrm{x}-5\right)\phantom{\rule{0ex}{0ex}}\mathrm{x}-5\mathrm{y}=-20.....\left(2\right)\phantom{\rule{0ex}{0ex}}\mathrm{Subtracting}\mathrm{both}\mathrm{the}\mathrm{equation},\mathrm{we}\mathrm{get}\phantom{\rule{0ex}{0ex}}4\mathrm{y}=44\phantom{\rule{0ex}{0ex}}\mathrm{y}=11\mathrm{years}\phantom{\rule{0ex}{0ex}}\mathrm{So}\mathrm{x}=35\mathrm{year}$

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