Product Constancy — Price, Consumption & Expenditure

The single most important formula in percentage word problems:

Price x Consumption = Expenditure

When any two of these three change, the ratio method gives you the answer instantly.

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The Core Concept: Ratio Multiplication

If Price has ratio P₁ : P₂ and Consumption has ratio C₁ : C₂, then:

Expenditure ratio = (P₁ × C₁) : (P₂ × C₂)

This works because Expenditure = Price × Consumption.

Example 1: Price rises by 15%, but Anil buys 20% fewer units. Overall spending change?

	Initial	Final
Price	20	23 (+15%)
× Consumption	5	4 (−20%)
= Expenditure	100	92

Change = (100 − 92)/100 × 100 = 8% decrease

Example 2: Cooking oil becomes 16.67% costlier. Priya reduces consumption by 28.57%. Expenditure change?

	Initial	Final
Price	6	7 (+16.67% = 1/6)
× Consumption	7	5 (−28.57% = 2/7)
= Expenditure	42	35 → simplified 6 : 5

Change = 1/6 × 100 = 16.67% decrease

Example 3: Product becomes 33.33% costlier, customer buys 10% fewer units.

	Initial	Final
Price	3	4 (+33.33%)
× Consumption	10	9 (−10%)
= Expenditure	30	36 → 5 : 6

Change = 1/5 × 100 = 20% increase

Example 4: Shop raises price by 30%. Riya can only buy 80% of planned quantity.

	Initial	Final
Price	10	13 (+30%)
× Consumption	5	4 (−20%)
= Expenditure	50	52 → 25 : 26

Change = 1/25 × 100 = 4% increase

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The Reciprocal Rule (Expenditure Constant)

When expenditure stays the same (same budget):

Price ratio and Consumption ratio are reciprocals of each other.

If price goes up in ratio 4 : 5, consumption must come down in ratio 5 : 4.

Why?

P₁ × C₁ = P₂ × C₂ (expenditure constant)

So: P₁/P₂ = C₂/C₁ → ratios are reciprocal.

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Finding Quantity Change (Budget Constant)

Example 5: Salary decreased by 40%. By what % must it increase to restore?

• Decrease 40% = 2/5. I : F = 5 : 3
• To go from 3 back to 5: increase = 2/3 × 100 = 66.67%

Example 6: Price decreases 20%, budget increases 10%. Quantity increase?

• Price: P₁ : P₂ = 5 : 4 (−20%)
• Expenditure: E₁ : E₂ = 10 : 11 (+10%)
• Consumption = Expenditure / Price
• C₁/C₂ = (E₁/P₁) / (E₂/P₂) = (10/5) / (11/4) = (10 × 4)/(5 × 11) = 40/55 = 8 : 11

Change = 3/8 × 100 = 37.5% increase

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Finding New Price Per Kg (Budget Constant)

Example 7: After 5.88% price cut in wheat, Neha buys 5 kg more with Rs. 6,800.

• 5.88% = 1/17. Price ratio = 17 : 16
• Budget constant → Consumption ratio (reciprocal) = 16 : 17
• Difference = 1 part = 5 kg → each part = 5 kg
• New consumption = 17 × 5 = 85 kg
• New price = 6800/85 = Rs. 80 per kg

Example 8: After 12.5% price cut in sugar, Priya buys 6 kg more with Rs. 2,400.

• 12.5% = 1/8. Price = 8 : 7
• Consumption (reciprocal) = 7 : 8. Difference = 1 part = 6 kg
• New consumption = 8 × 6 = 48 kg
• Reduced price = 2400/48 = Rs. 50 per kg

Example 9: After 9.09% price increase, Meena buys 4 kg less with Rs. 2,640.

• 9.09% = 1/11. Price = 11 : 12
• Consumption (reciprocal) = 12 : 11. Difference = 1 part = 4 kg
• New consumption = 11 × 4 = 44 kg
• Increased price = 2640/44 = Rs. 60 per kg

Example 10: After 25% price increase, with Rs. 2,400, quantity purchased is 8 litres less.

• 25% = 1/4. Price = 4 : 5
• Consumption = 5 : 4. Difference = 1 part = 8 litres
• Old consumption = 5 × 8 = 40 litres, New = 32 litres
• Increased price = 2400/32 = Rs. 75 per litre

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Successive Price Changes + Constant Budget

Example 11: Rice price reduced by 20% then again by 10%. With Rs. 1,800, quantity bought is 7 kg more. Original price per kg?

• Successive price change: I : F = 5/4 × 10/9 → Price I : F = 25 : 18
• Consumption (reciprocal) = 18 : 25. Difference = 7 parts = 7 kg → 1 part = 1 kg
• New consumption = 25 kg
• Original price = 1800/18 = Rs. 100 per kg

Example 12: Rice price increases 25%. Person buys same 40 kg, pays Rs. 500 more.

• Price = 4 : 5, Consumption = 1 : 1 (same)
• Expenditure = 4 : 5. Difference = 1 part = Rs. 500
• Old expenditure = 4 × 500 = Rs. 2,000
• Original price = 2000/40 = Rs. 50 per kg

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Revenue Problems (Price × Quantity = Revenue)

The same framework applies to ticket pricing, product pricing, etc.

Example 13: Cinema increases ticket price by 6.67%. Viewers decrease by 12.50%. Revenue change?

	Initial	Final
Price	15	16
× Viewers	8	7
= Revenue	120	112 → 15 : 14

Change = 1/15 × 100 = 6.67% decrease

Example 14: Museum raises ticket price by 22.22%. Visitors fall by 25%. Revenue change?

	Initial	Final
Price	9	11
× Visitors	4	3
= Revenue	36	33 → 12 : 11

Change = 1/12 × 100 = 8.33% decrease

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Quick Reference

Scenario	Method
Both price & consumption change	Multiply ratios → find expenditure ratio
Expenditure constant	Price and consumption ratios are reciprocal
Find quantity from "X kg more/less"	Get consumption ratio → difference = given kg
Find new price per kg	New price = Budget / New consumption
Revenue problems	Same as Price × Consumption = Expenditure

Exam tip: Always write the Initial : Final ratio table for Price and Consumption. Multiply across. Simplify. The answer appears instantly.