Question

parul is one-fifth the age, her mother was 15 years ago and parul’s brother is three-fifths the, age her mother was 10 years ago. if the sum of parul’s and her brother’s ages is 31, then how old is parul’s mother?

Answer 1

Let Parul's mother age be 'x' years.

Parul is one-fifth the age, her mother was 15 years ago

Parul's mother age 15 years ago = (x-15) years.

Therefore, Parul's age = $\frac{1}{5} (x-15)$

Parul's brother is three-fifths the, age her mother was 10 years ago

Parul's mother age 10 years ago = (x-10) years.

Therefore, Parul's age = $\frac{3}{5} (x-10)$

Now, the sum of parul's and her brother's age is 31.

So, $\frac{1}{5}(x-15)+\frac{3}{5}(x-10)=31$

$\frac{x-15+3x-30}{5}=31$

$4x-45 = 155$

4x = 200

x = 50

Therefore, the Parul's mother age is 50 years.