Age Proportion of Three Friends

Let the ages of the three friends be $2x$, $3x$, and $5x$.

The sum of their ages = $3 \times 20 = 60$ years.

$2x + 3x + 5x = 60 \implies 10x = 60 \implies x = 6$

The age of the oldest friend is $5x = 5 \times 6 = 30$ years.