Single correct option
The price of cooking gas rises by 25%. By what percentage must a household cut its consumption so that its expenditure on gas rises by only 10%?
- A. 10%
- B. 12%
- C. 15%
- D. 8%
Show answer and solution
Answer: (B) 12%
Expenditure = Price × Consumption. Let the original price and consumption both be 1, so expenditure = 1.
New price = 1.25 and the target expenditure = 1.10. New consumption = 1.10/1.25 = 0.88.
So consumption must fall from 1 to 0.88, a cut of 12%.
Why not 15%? 15% is simply 25% − 10%, the common trap of subtracting percentages; percentage changes multiply, they do not add.
Tip: Required multiplier on consumption = (1 + target change)/(1 + price change).
New price = 1.25 and the target expenditure = 1.10. New consumption = 1.10/1.25 = 0.88.
So consumption must fall from 1 to 0.88, a cut of 12%.
Why not 15%? 15% is simply 25% − 10%, the common trap of subtracting percentages; percentage changes multiply, they do not add.
Tip: Required multiplier on consumption = (1 + target change)/(1 + price change).
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