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If the price of petrol increases by 25%, by how much percent should a consumer reduce consumption to keep the expenditure same?
15%
20%
25%
30%
20%
Use the fraction conversion: 25% = 1/4. To keep expenditure same, decrease the consumption by 1/(4+1) = 1/5, which equals 20%.
Increase in price of petrol = 25%. Total expenditure remains constant.
Reduction%=100+RRтАЛ├Ч100
Use the fraction conversion: 25% = 1/4. To keep expenditure same, decrease the consumption by 1/(4+1) = 1/5, which equals 20%.
Many students incorrectly assume the reduction is also 25%, failing to realize that the percentage decrease must be calculated on the new (increased) price.
Identify parameters
Let the original price be 100 and consumption be 100 units. Original expenditure = 100 * 100 = 10000.
PricenewтАЛ=125
Apply percentage reduction formula
To maintain the same expenditure, let the new consumption be CnewтАЛ. Thus, 125├ЧCnewтАЛ=10000.
CnewтАЛ=12510000тАЛ=80
Calculate percentage reduction
Reduction = Original - New = 100 - 80 = 20. In percentage terms, this is 20/100 * 100.
Reduction=20%
B is correct because the reduction in consumption required to offset a 25% price increase is exactly 20%.
This concept of inverse proportion is identical to time and speed problems where distance is constant; if speed increases by x%, time reduces by the same formula.
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