Question

A mother is 24 years older than her daughter.before seven years she was seven times her daughter's find their present age​

Answer 1

$\large\bf{\underline{\underline{Answer:}}}$

$\small\textbf\color{red}{Mother's Present Age}$$\small\bold{ = 36\: years}$

$\small\textbf\color{red}{Daughter's Present Age}$$\small\bold{ = 12\: years}$

$\underline{\bf{Explanation\::}}$

Let present age of mother be "m" and present age of daughter be "d"

Mother is 24 years older than her daughter,

$\small\color{magenta}{So \:we \:can\: write:}$

$\underline{\boxed{\sf\purple{m = 24 + d}}}$

8 years ago, Mother was 7 times old as daughter, that would be:

$\underline{\boxed{\sf\purple{m - 8 = 7(d - 8)}}}$

$\bold{Note, }$

since 8 years ago, both "m" and "d" have 8 subtracted from it.

Now we substitute Equation 1 into Equation 2 and solve for d:

$\begin{gathered}m - 8 = 7(d - 8)\\24+d - 8 = 7(d - 8)\\16+d=7d-56\\6d=72\\d=\frac{72}{6}\\d=12\end{gathered}$

$\green{\bf {Mother \:age\:, m, \:would\: be:}}$

$\mapsto$$\sf{m = 24 + d}$

$\mapsto$$\sf{m = 24 + 12}$

$\mapsto$$\sf{m = 36}$

$\bold{Hence,}$

Mother's Present Age =$\color{red}{36 \:years}$

Daughter's Present Age = $\color{red}{12\: years}$

Thankyou :)