If a merchant offers a discount of 40% on the list price, then he makes a loss of 10%. What % profit or % loss will he make if he sells at a discount of 20% of the list price?

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

After 40% discount, selling price = $$\frac{100 - 40}{100} \times 100x$$ = Rs. $$60x$$

Let Cost price = Rs. $$y$$

=> Loss % = $$\frac{y - 60x}{y} \times 100 = 10$$

=> $$\frac{y - 60x}{y} = \frac{10}{100} = \frac{1}{10}$$

=> $$10y - 600x = y$$

=> $$10y - y = 600x$$

=> $$y = \frac{600x}{9} = 66.67x$$

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

$$\therefore$$ Profit % = $$\frac{80x - 66.67x}{66.67x} \times 100$$

= $$19.99 \approx 20 \%$$