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.

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Please find below the solution to the asked query :
$$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{ages} \mathrm{of} \mathrm{Mira} \mathrm{and} \mathrm{fathers} \mathrm{are} \mathrm{y} \mathrm{and} \mathrm{x} \\ \mathrm{x}-\mathrm{y} = 24 .....\left(1\right) \\ \mathrm{now} \mathrm{ages} \mathrm{five} \mathrm{years} \mathrm{ago} \mathrm{was} \\ \mathrm{x}-5, \mathrm{y}-5 \\ \mathrm{Now} \mathrm{according} \mathrm{to} \mathrm{the} \mathrm{question}, \\ \mathrm{y}-5 = \frac{1}{5}\left(\mathrm{x}-5\right) \\ \mathrm{x}-5\mathrm{y}=-20.....\left(2\right) \\ \mathrm{Subtracting} \mathrm{both} \mathrm{the} \mathrm{equation}, \mathrm{we} \mathrm{get} \\ 4\mathrm{y} = 44 \\ \mathrm{y} = 11 \mathrm{years} \\ \mathrm{So} \mathrm{x} =35 \mathrm{year} \end{gathered}$$


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