Question

The sum of the present ages of mother and her daughter is $50$ years. After $20$ years, mother's age will be twice her daughter's age at the time. Find their present ages.

Answer 1

Let $x$ and $y$ be the present age of mother and her daughter.

Therefore,

$x+y=50$

$\Rightarrow x=50-y.....\left(1\right)$

After $20$ years, mother's age will be twice her daughter's age at the time.

$x+20=2(y+20)$

$\Rightarrow x-2y=20.....\left(2\right)$

From equation $\left(1\right)\&\left(2\right)$, we have

$50-y-2y=20$

$3y=30$

$\Rightarrow y=10$

Substituting the value of $y$ in equation $\left(1\right)$, we get

$x=50-10=40$

Hence the present age of mother and her daughter is $40$ and $10$ years respectively.