If the price of the commodity is increased by 50% by what fraction must its consumption be reduced so as to keep the same expendi…

Question

If the price of the commodity is increased by 50% by what fraction must its consumption be reduced so as to keep the same expenditure on its consumption?

1. A. 1/4
2. B. 1/3 (Correct answer)
3. C. 1/2
4. D. 2/3

Correct Answer

Option B — 1/3

Detailed Solution & Explanation

The correct answer is 1/3.

Key Points

• Expenditure = Price x Consumption. To hold expenditure constant when price rises, consumption must fall in the inverse proportion.
• Let the original price be 100 and consumption be 100, so expenditure = 10,000.
• New price = 150. Required consumption = 10,000 / 150 = 66.67.
• Reduction = 100 - 66.67 = 33.33, which as a fraction of the original consumption is 33.33/100 = 1/3.

Additional Information

• The standard shortcut for a price rise of R% is: reduction in consumption = R / (100 + R).
• Here R = 50, so the reduction = 50 / 150 = 1/3 — one step instead of four.
• Watch the direction: a price fall of R% permits an increase of R / (100 - R).