Question

Age of a mother is 1/4 the age of her daughter. If the difference of their ages is
36 years, find their ages.
Mother__yrs
Daughter__yrs​

Answer 1

Correct question:-

Age of a daughter is 1/4 the age of her mother. If the difference of their ages is 36 years, find their ages.

Answer:-

The age of Mother is 48 years and the age of daughter is 12 years.

Explanation :-

Given :

Age of mother = 1/4th the age of daughter.

Difference of their ages = 36

To find :

The age of Mother and daughter

Solution :

Let the age of daughter be x

and the age of mother be 4x

According to question,

$= > 4x - x = 36$

$= > 3x = 36$

$= > x = \dfrac{36}{3}$

$= > x = 12$

Hence the age of the daughter is = 12 years

And the age of the mother is => 4×12 = 48 years

Answer 2

Correct Question :-

Age of a daughter is 1/4 the age of her mother. If the difference of their ages is 36 years, find their ages.

Answer :-

Age of mother is 48 years and age of daughter is 12 years

Solution :-

Let the age of mother be 'x' years

Age of daughter = 1/4 the age of her mother = 1/4 of x = 1/4 * x = x/4 years

Difference of their ages = 36 years

⇒ x - x/4 = 36

$\tt \implies x - \dfrac{x}{4} = 36$

Taking LCM of LHS

$\tt \implies \dfrac{x(4)}{1(4)} - \dfrac{x}{4} = 36$

$\tt \implies \dfrac{4x}{4} - \dfrac{x}{4} = 36$

$\tt \implies \dfrac{4x - x}{4} = 36$

$\tt \implies \dfrac{3x}{4} = 36$

$\tt \implies 3x = 36 \times 4$

$\tt \implies 3x = 144$

$\tt \implies x = \dfrac{144}{3}$

$\tt \implies x =48$

Therefore age of mother = x = 48 years

Age of daughter = x/4 = 48/4 = 12 years

Verification :-

$\tt x - \dfrac{x}{4} = 36$

$\tt \implies 48 - 12 = 36$

$\tt \implies 36 = 36$