Question

A person’s present age is 2/5 of the age of his mother. After 8 years, he will be
one - half of the age of his mother. How old is the mother at present​

Answer 1

$★ {\pmb{\underline{\sf{Required \ Solution ... }}}}$

Let the Present age of the Mother be x and Present age of the Person be ${\tt{ \dfrac{2x}{5} }}$.

★ After 8 years,

• Mother's Age = (x + 8)
• Person's Age = (⅖x + 8)

$\circ \ {\pmb{\underline{\sf{ According \ to \ Question: }}}} \\ \\ \\ \colon\implies{\tt{ \dfrac{1}{2} (x+8) = \dfrac{2x}{5} + 8 }} \\ \\ \\ \colon\implies{\tt{ \dfrac{x+8}{2} = \dfrac{2x+40}{5} }} \\ \\ \\ \colon\implies{\tt{ 5(x+8) = 2(2x+40) }} \\ \\ \\ \colon\implies{\tt{ 5x + 40 = 4x + 80 }} \\ \\ \\ \colon\implies{\tt{ 5x-4x = 80-40 }} \\ \\ \\ \colon\implies{\tt{ x = 40 \ Years }}$

Hence,

The Present age of the Mother will be 40 Years.