If a merchant offers a discount of 30% on the list price, then he makes a loss of 16%. 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 30% discount, selling price = $$\frac{100 - 30}{100} \times 100x$$ = Rs. $$70x$$

Let Cost price = Rs. $$y$$

=> Loss % = $$\frac{y - 70x}{y} \times 100 = 16$$

=> $$\frac{y - 70x}{y} = \frac{16}{100} = \frac{4}{25}$$

=> $$25y - 1750x = 4y$$

=> $$25y - 4y = 1750x$$

=> $$y = \frac{1750x}{21} = 83.33x$$

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

$$\therefore$$ Loss % = $$\frac{83.33x - 80x}{83.33x} \times 100$$

= $$3.99 \approx 4 \%$$

=> Ans - (B)