Allowing a discount of 25% on the marked price of a mixer still leaves a shopkeeper a profit of 20%. If he wants a profit of 40% on the same mixer, the discount he can allow is what percent?

Take the cost as ₹100. Then the selling price is ₹120 and 0.75 × marked price = 120, so the marked price is ₹160. For a 40% profit he needs ₹140, so the discount is 20/160 = 12.5%. Trading percentage points one for one (profit up 20 points, so discount down 20 points, giving 5%) is wrong — the discount is reckoned on ₹160 and the profit on ₹100. Working out 20/140 gives 14.3%, the reduction as a percent of the selling price.