If a merchant offers a discount of 25% on the list price, then he makes a loss of 5%. What % profit or % loss will he make if he sells at a discount of 10% of the list price?

Let list price = Rs. $$100x$$

After 25% discount, selling price = $$\frac{100 - 25}{100} \times 100x$$ = Rs. $$75x$$

Let Cost price = Rs. $$y$$

=> Loss % = $$\frac{y - 75x}{y} \times 100 = 5$$

=> $$\frac{y - 75x}{y} = \frac{5}{100} = \frac{1}{20}$$

=> $$20y - 1500x = y$$

=> $$20y - y = 1500x$$

=> $$y = \frac{1500x}{19} \approx 79x$$

If discount = 10%, => Selling price = $$\frac{100 - 10}{100} \times 100x = Rs. 90x$$

$$\therefore$$ Profit % = $$\frac{90x - 79x}{79x} \times 100$$

= $$13.92 \approx 14 \%$$