The selling price of 12 pens is equal to the cost price of 15 pens. If the selling price is increased by 10%, what would be the next profit percentage on selling one pen?

Let's take the selling price and cost price of 1 pen to be $$s$$ nd $$c$$ respectively. 

We have the equation $$12s=15c$$, which would give te ratio of selling price to cost price as $$\frac{s}{c}=\frac{15}{12}=\frac{5}{4}$$

Essentially, if the cost price is 4, the selling price is 5

If we increase the selling price by 10%, it becomes 5.5

This would give us a profit of 1.5 per pen

Profit percentage would be $$\frac{1.5}{4}\times\ 100=1.5\times\ 25=37.5\%$$

Therefore, Option D is the correct answer.