Question

The ages of two persons differ by $16$ years. If $6$ years ago, the elder one be $3$ times as old as the younger one, find their present ages.

• A. 15 years and 31 years
• B. 14 years and 30 years
• C. 12 years and 28 years
• D. 10 years and 26 years

Answer 1

The correct option is B 14 years and 30 years

Let the age of younger person be $x$ years.

$\therefore$ Age of elder person $=16+x$ years$

$6$ years ago,

Age of younger person $=(x-6)$ years

Age of elder person $=(16+x-6)$ years

$=(10+x)$ years

According to question, $x+10=3(x-6)$

$\Rightarrow x+10=3x-18\Rightarrow 2x=28$

$\Rightarrow x=14$

$\therefore$ Age of younger person $=14$ years

Age of elder person $=(14+16)$ years

$=30$ yeras