Question

$20$ years ago, when my parents got married, their average age was $23$ years, now the average age of my family, consisting of myself and my parents only is $34$ years. My present age is

• A. $34$ years
• B. $42$ years
• C. $24$ years
• D. $16$ years

Answer 1

The correct option is D $16$ years

Let the present age of parents be $x,y$ and

present age of child be $z$

$20$ years ago the age of parenst is $x-20,y-20$

Given that, 20 years ago the average age of the parents is $23$.

$⟹\frac{x-20+y-20}{2}=23⟹x+y-40=46$

$⟹x+y=46+40=86$ ———-(1)

Given, that average age of the family at present is $34$.

$⟹\frac{x+y+z}{3}=34⟹x+y+z=34\times 3=102$ ———(2)

Substituting (1) in (2) we get

$86+z=102⟹z=102-86=16$

Therefore the present age is $16$ years