Question

If twice the age of the daughter is added to age of her mother, the result is 56. But if twice the age of the mother is added to the age of the daughter, the result is 82. What is the present age of the mother and her daughter?

• A. 36 years, 10 years
• B. 35 years, 11 years
• C. 38 years, 9 years
• D. 33 years, 8 years

Answer 1

The correct option is A

36 years, 10 years

Let, the age of mother be $x$ years and age of daughter be $y$ years.

According to the given connditions
$x+2y=56$ ______(1)
$2x+y=82$ ______(2)

Finding $x$ from equation (1)
$\Rightarrow x=56-2y$ ______(3)

Putting this value in equation (2)
$\Rightarrow 2(56-2y)+y=82$
$\Rightarrow 112-4y+y=82$
$\Rightarrow -3y=-30$
$\Rightarrow y=10$

Putting this value of $y$ in equation (3)
$\Rightarrow x=56-20$
$\Rightarrow x=36$

Therefore, Mother's age = 36 years
Daughters age = 10 years