Question

The age of Varsha is one third of the age of her mother. The sum of their ages is 48 years. Then what is the age of her mother?​

Answer 1

• The age of her mother = 36 years.

Given :

• The age of Varsha is one third of the age of her mother.
• The sum of their ages = 48.

To Find :

• The age of her mother.

Solution :

Let,

The age of her mother be x.

The age of Varsha be x / 3 because according to the question, the age of Varsha is one third of the age of her mother.

Given,

The sum of their ages is 48.

That means,

Age of her mother + Age of Varsha = 48

$\bf \implies x+\dfrac{x}{3}=48\\\\\\\bf\implies \dfrac{(x\times3)+(x\times1)}{3}=48\\\\\\\bf \implies\dfrac{3x+x}{3}=48\\\\\\\bf \implies\dfrac{4x}{3}=48\\\\\\\bf\implies4x=48 \times3\\\\\\\bf\implies4x=144\\\\\\\bf\implies x= \frac{\not144}{\not4}\\\\\\\bf\implies x=\dfrac{36}{1} \\\\\\\bf\implies x=36\\\\\\\:\:\therefore\:\:\bf\: x =36\:years$

So, the age of Varsha and her mother are :

★ The age of her mother = x = 36 years.

★ The age of Varsha = x / 3 = 36 / 3 = 12 years.

Hence,

The age of her mother is 36 years.

Answer 2

$\bf{\underline{ \underline{Given :- }}}$

• The age of Varsha is one third of the age of her mother.
• The sum of their ages is 48 years.

$\bf{\underline{ \underline{To \: Find :- }}}$

• The age of her mother.

$\bf{\underline{ \underline{Solution :- }}}$

Let her mother's age be $x$

According to the 1st condition,

Varsha's age is $\frac{x}{3} \:$ years.

According to the 2nd condition,

$x + \frac{x}{3} = 48$

$⇒ \frac{3x + x}{3} = 48$

$⇒4x = 144$

$⇒x =36$

$\sf\red{Therefore,\: Mother's\: age \:is \:36\: years.}$