If the cost price of 15 pencils is equal to the selling price of 10 pencils, what is the gain or loss percentage?

Let's assume the cost price and selling price of each pencil is 'SP and 'CP'.
If the cost price of 15 pencils is equal to the selling price of 10 pencils.

15CP = 10SP

3CP = 2SP

$$\frac{CP}{SP}\ =\ \frac{2}{3}$$

Here SP is more than CP. So there will be profit.

Let's assume SP = 3y and CP = 2y

Gain(profit) percentage = $$\frac{\left(SP-CP\right)}{CP}\times\ 100$$

= $$\frac{\left(3y-2y\right)}{2y}\times\ 100$$

= $$\frac{y}{2y}\times100$$

= 50%