The price of milk rises by 20%. By what percentage must a family reduce its consumption so that its spending on milk 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 120, so the quantity must become 10,000 ÷ 120 = 83.33. That is a cut of 16.67%. Shortcut: reduction % = rise ÷ (100 + rise) × 100 = 20 ÷ 120 × 100. Cutting by 20% would leave the family spending less than before.