Question

Balu is $x$ years old. His sister is $4\frac{1}{2}$ times older than him whereas his uncle is $30$ years older than him. If the total of their ages is $56$ years, what is the value of $x$?

• A. $12$
• B. $10$
• C. $8$
• D. $4$

Answer 1

The correct option is D $4$

Given : Balu is $x$ years old .

His sister is $4\frac{1}{2}=\frac{9}{2}$ times older than Balu.

Then his sister's age $=\frac{9}{2}\times x=\frac{9x}{2}$

His uncle is $30$ years older than Balu

Then age of his uncle $=x+30$

Given total of their ages is $56$ years

$\therefore x+\frac{9x}{2}+(x+30)=56$

$\Rightarrow 2x+9x+2x+60=112$

$\Rightarrow 2x+9x+2x=112-60$

$\Rightarrow 13x=52$

$\Rightarrow x=4$