The price of sugar rises by 25%. By what percentage must a family reduce its consumption so that its spending on sugar stays the same?

💡 Solution & Explanation

Spending = price × quantity. Take the old price as 100 and the old quantity as 100, so the spending is 10,000. The new price is 125, so the quantity must become 10,000 ÷ 125 = 80. That is a cut of 20%. Shortcut: reduction % = rise ÷ (100 + rise) × 100 = 25 ÷ 125 × 100. Cutting by 25% would leave the family spending less than before.