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Price Rise and Consumption Cut: The Product Constancy Rule

Constant expenditure • Fraction shortcut • Price fall • Limited budget • Area and speed

SSC Banking Railway 📅 Last updated: 2026-10-20

When the price of something goes up, how much less should you buy so that your total bill stays the same? Questions phrased as "if the price increases by 25%, by how much must consumption decrease" all rest on one fact: expenditure = price × consumption. If expenditure is to stay fixed, the two factors must move in opposite directions so that their product does not change. This is called product constancy.

The cut is not equal to the rise. A 25% rise followed by a 25% cut leaves you spending 1.25 × 0.75 = 0.9375 of the original, so you would be under budget. The correct cut is smaller.

Let the price rise by r%. The new price is (1 + r/100) times the old. For the product to stay the same, the new consumption must be 1 ÷ (1 + r/100) = 100/(100 + r) of the old. The cut is therefore 1 − 100/(100 + r) = r/(100 + r).

Price rises r% → cut consumption by r/(100 + r) × 100%
Price falls r% → raise consumption by r/(100 − r) × 100%

Worked example 1: a 25% price rise

Cut = 25/125 × 100 = 20%. Check: 1.25 × 0.80 = 1, so spending is unchanged.

Worked example 2: a 20% price fall

Consumption can rise by 20/80 × 100 = 25%. Check: 0.80 × 1.25 = 1.

Write the percentage as a fraction 1/n and the answer appears at once. A rise of 1/n needs a cut of 1/(n + 1); a fall of 1/n allows a rise of 1/(n − 1).

Price rises byCut consumption byPrice falls byRaise consumption by
10% (1/10)9.09% (1/11)10% (1/10)11.11% (1/9)
20% (1/5)16.67% (1/6)20% (1/5)25% (1/4)
25% (1/4)20% (1/5)25% (1/4)33.33% (1/3)
50% (1/2)33.33% (1/3)50% (1/2)100% (1/1)

Learning this table of fractions helps across percentage, profit and ratio questions, not only this one.

If the question gives both changes and asks about expenditure, multiply the two factors.

Worked example 3: price up 20%, consumption down 10%

New expenditure = 1.2 × 0.9 = 1.08 of the old, an 8% increase.

If the budget is allowed to grow by a fixed percentage, divide the new budget factor by the new price factor to get the consumption factor.

Worked example 4: a limited budget increase

The price rises by 40% and the budget by 12%. New consumption = 1.12 ÷ 1.40 = 0.8 of the old, a cut of 20%.

When the price rises twice, combine the rises into one factor first and then apply the rule. Do not add the two percentages.

Worked example 5: two successive rises

A price rises by 25% and then by a further 20%. The combined factor is 1.25 × 1.2 = 1.5, a 50% rise in all. To keep spending unchanged, consumption must fall by 1 − 1/1.5 ≈ 33.33%.

A related question gives a fixed sum of money and asks for the original price. "A 20% fall in the price of sugar lets a buyer get 5 kg more for ₹800. What was the original price per kg?" The fall saves 20% of ₹800, which is ₹160, and that saving buys the extra 5 kg at the new price.

Worked example 6: extra quantity for a fixed sum

New price = ₹160 ÷ 5 = ₹32 a kg. That is 80% of the original price, so the original price was 32 ÷ 0.8 = ₹40 a kg. Check: ₹800 buys 20 kg at ₹40 and 25 kg at ₹32, which is 5 kg more.

Any pair of quantities whose product is fixed obeys the same rule. For a rectangle of fixed area, length and breadth trade off. For a fixed distance, speed and time trade off.

Worked example 7: area

If a rectangle's length grows by 30%, the breadth must shrink by 30/130 × 100 ≈ 23.08% to keep the area unchanged.

Worked example 8: speed and time

If a car's speed falls by one-sixth, it covers the same distance in 1 ÷ (5/6) = 6/5 of the time, an increase of 20%.

  • ✘ Cutting consumption by the same percentage as the price rise.
  • ✘ Adding percentages when both factors change. Multiply the factors instead.
  • ✘ Confusing the base: the cut is a share of the old consumption.

Successive percentage changes work the same way; see the successive discount formula. For time and distance, see average speed, and for more formulas the Quant cheat code.

Q1. The price of petrol rises by 20%. By how much must a driver cut consumption to keep spending the same? easy

✅ Answer: (b) 16.67%

💡 Explanation: Cut = r/(100 + r) × 100 = 20/120 × 100 = 16.67%. With fractions, a 1/5 rise needs a 1/6 cut.

Q2. The price of sugar falls by 10%. By how much can a family increase consumption without spending more? easy

✅ Answer: (a) 11.11%

💡 Explanation: Rise = r/(100 − r) × 100 = 10/90 × 100 = 11.11%. A 1/10 fall allows a 1/9 rise.

Q3. The price of a commodity rises by 25% and a household cuts its consumption by 15%. What happens to its expenditure? medium

✅ Answer: (c) 6.25% increase

💡 Explanation: Expenditure = price × quantity, so the new spending is 1.25 × 0.85 = 1.0625 times the old: a 6.25% increase.

Q4. The length of a rectangle is increased by 50%. By what percentage must the breadth be reduced to keep the area unchanged? easy

✅ Answer: (d) 33.33%

💡 Explanation: Area = length × breadth, so the same rule applies: 50/150 × 100 = 33.33%. A 1/2 rise needs a 1/3 cut.

Q5. Walking at 4/5 of his usual speed, a man reaches the office 15 minutes late. What is his usual time for the walk? medium

✅ Answer: (a) 60 minutes

💡 Explanation: Speed × time is fixed, so at 4/5 of the speed the time becomes 5/4 of usual. The extra quarter is 15 minutes, so the usual time is 60 minutes.

Q6. The price of rice rises by 50%, but a family can raise its rice budget by only 20%. By what percentage must it cut consumption? hard

✅ Answer: (c) 20%

💡 Explanation: New quantity = new budget ÷ new price = 1.2 ÷ 1.5 = 0.8 of the old quantity, a 20% cut.

Why is the cut smaller than the price rise?

The cut is measured on the old, larger consumption, while the rise is measured on the old, smaller price. Undoing a 25% increase means removing one-fifth of the new total, which is 20% of the original consumption.

Where else does the product constancy rule apply?

Anywhere two quantities multiply to a fixed total: price and quantity for expenditure, length and breadth for area, speed and time for a fixed distance, and workers and days for a fixed job.

All problems and solutions on this page are original. No outside facts are relied on; every numeric answer is recomputed by software before publishing.

How this page was prepared. Drafted with AI assistance (Claude (Anthropic AI model)) from the sources listed above. 14 calculations on this page were recomputed by software and matched. Automated checks also covered structure, internal links and duplicate text. Software checks cannot confirm facts. Reviewed by praveen on 2026-10-20 against the sources listed above.

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