Let c = cost of item, s = selling price.
Since we're given that the profit was initially 20% of the cost, we can set up the equation:
$0.2c = s - c$

We're also given that the initial selling price was $60, so plugging back into the equation, we can find the cost:
$0.2c + c = 60$
$1.2c = 60$
$c = 60/1.2 = 50$

Since we're told that c remains the same, the new profit is:
$= 65-50 =15$

Thus, the percentage of the new profit of the item over the cost of the item is:
$\frac{15}{50}=$ 30%