Question

If Dennis is ${\left(\frac{1}{3}\right)}^{rd}$ the age of his father Keith now and was ${\left(\frac{1}{4}\right)}^{th}$ the age of his father $5$ years ago then how old will his father Keith be $5$ years from now?

• A. $20$ years
• B. $45$ years
• C. $40$ years
• D. $50$ years

Answer 1

The correct option is D $50$ years

Let keith's age now be $x$ years. Then
Dennis's age now $=\frac{x}{3}$ years
Keith's age $5$ years ago $=(x-5)$ years
Dennis's age 5 years ago $=(\frac{x}{3}-5)$ years
Given, $(\frac{x}{3}-5)=\frac{1}{4}(x-5)$

$\Rightarrow \frac{x-15}{3}=\frac{x-5}{4}$
$\Rightarrow 4x-60=3x-15$
$\Rightarrow x=45$
$\therefore$ Keith's age $5$ years from now $=(45+5)$ years $=50$ years