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If the price of sugar decreases by 20%, then by what percentage must a householder increase her consumption of sugar so as to leave her expenditure on sugar unchanged?
3331тАЛ%
1632тАЛ%
25%
20%
25%
Use the fraction conversion: 20% is 1/5. If price decreases from 5 to 4, quantity must increase from 4 to 5 (a gain of 1 on 4), which is 1/4 = 25%.
The price of sugar decreases by 20%, and the total expenditure is to remain unchanged.
Percentage┬аincrease=(100тИТrrтАЛ)├Ч100
Use the fraction conversion: 20% is 1/5. If price decreases from 5 to 4, quantity must increase from 4 to 5 (a gain of 1 on 4), which is 1/4 = 25%.
Students often mistakenly answer 20% by assuming that a 20% decrease must be balanced by a 20% increase, ignoring the change in the base value.
Define the relationship
Let initial price be P and initial consumption be C. Initial expenditure E=P├ЧC. New price PтА▓=PтИТ0.2P=0.8P.
PтА▓=0.8P
Set constant expenditure
To keep expenditure E unchanged, let new consumption be CтА▓. So, 0.8P├ЧCтА▓=P├ЧC.
CтА▓=0.8CтАЛ=1.25C
Calculate percentage increase
The increase in consumption is CтА▓тИТC=1.25CтИТC=0.25C. Converting this to a percentage relative to C: (0.25/1)├Ч100=25%.
Increase=25%
C is correct because a 20% decrease in price requires a 25% increase in consumption to maintain the same expenditure level.
This concept of 'price vs consumption' is identical to 'speed vs time' problems where distance is constant; if speed decreases, time must increase by the same logic.