If a merchant offers a discount of 4% on the list price, then she makes a loss of 10%. What % profit or % loss will she make if she sells at a discount of 20% of the list price?

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

After 4% discount, selling price = $$\frac{96}{100} \times 100x$$ = Rs. $$96x$$

Let Cost price = Rs. $$y$$

=> Loss % = $$\frac{y - 96x}{y} \times 100 = 10$$

=> $$\frac{y - 96x}{y} = \frac{10}{100} = \frac{1}{10}$$

=> $$10y - 960x = y$$

=> $$10y - y = 960x$$

=> $$y = \frac{960x}{9} = 106.67x$$

If discount = 20%, => Selling price = $$\frac{80}{100} \times 100x = Rs. 80x$$

$$\therefore$$ Loss % = $$\frac{106.67x - 80x}{106.67x} \times 100$$

$$\approx 25 \%$$