If a merchant offers a discount of 20% on the list price, then she makes a loss of 16%. What % profit or % loss will she make if she sells goods at a discount of 10% of the list price?

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

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

Let Cost price = Rs. $$y$$

=> Loss % = $$\frac{y - 80x}{y} \times 100 = 16$$

=> $$\frac{y - 80x}{y} = \frac{16}{100} = \frac{4}{25}$$

=> $$25y - 2000x = 4y$$

=> $$25y - 4y = 2000x$$

=> $$y = \frac{2000x}{21} = 95.23x$$

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

$$\therefore$$ Loss % = $$\frac{95.23x - 90x}{95.23x} \times 100$$

= $$5.49 \approx 5.5 \%$$