If a merchant offers a discount of 20% on the list price, then he makes a loss of 10%. What % profit or % loss will she make if he sells at a discount of 5% of the list price?

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

After 20% discount, selling price = $$\frac{80}{100} \times 100x$$ = Rs. $$80x$$

Let Cost price = Rs. $$y$$

=> Loss % = $$\frac{y - 80x}{y} \times 100 = 10$$

=> $$\frac{y - 80x}{y} = \frac{10}{100} = \frac{1}{10}$$

=> $$10y - 800x = y$$

=> $$10y - y = 800x$$

=> $$y = \frac{800x}{9} = 88.89x$$

If discount = 5%, => Selling price = $$\frac{95}{100} \times 100x = Rs. 95x$$

$$\therefore$$ Profit % = $$\frac{95x - 88.89x}{88.89x} \times 100$$

$$\approx 6.875 \%$$