If the price of sugar rises by 25%, by what percentage must a family cut its consumption to keep its spending the same?
By 20%. Spending = price x quantity. If price becomes 125/100 of the old price, quantity must become 100/125 = 4/5, a cut of 1/5, which is 20%. Formula: r / (100 + r) x 100 = 25/125 x 100 = 20%.
Explain it simply
Your monthly budget for sugar is fixed, say ₹500. If each kilo now costs more, you must buy fewer kilos. The cut is not the same 25%, because the rise was measured on the old price while the cut is measured on the old quantity. A 25% rise means the price went from 4 parts to 5 parts, so the quantity has to go from 5 parts to 4 parts.
Example
Question: Sugar price rises 25%. By what percentage should consumption fall so spending stays the same?
- Let old price = ₹40/kg and old consumption = 10 kg. Spending = ₹400.
- New price = 40 x 1.25 = ₹50/kg.
- To spend ₹400: 400 / 50 = 8 kg.
- Cut = 2 kg out of 10 kg = 20%.
Shortcut: cut % = r / (100 + r) x 100 = 25 / 125 x 100 = 20%. If the price falls by r%, consumption can rise by r / (100 - r) x 100. A 20% fall allows a 25% rise.
const r = 25;
console.log((r / (100 + r)) * 100); // Output: 20What to say in the interview
"Spending is price times quantity, so if price is multiplied by 5/4, quantity must be multiplied by 4/5. That is a 20% cut. The general formula is r over 100 plus r, times 100."
Common mistakes
- Answering 25%. The percentages are on different bases.
- Using 100 - r in the denominator for a price rise; that version is for a price fall.