Question
Download Solution PDFIf 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The price of sugar decreases by 20%.
Formula Used:
To keep the expenditure unchanged: (Original Price × Original Quantity) = (New Price × New Quantity)
Calculation:
Let the original price be P and the original quantity be Q.
New Price = P - 0.20P = 0.80P
Let increase consumption of sugar = x%
New Quantity = Q + x% of Q = Q(1 + x/100)
Expenditure remains unchanged:
PQ = 0.80P × Q(1 + x/100)
⇒ Q = 0.80Q(1 + x/100)
⇒ 1 = 0.80(1 + x/100)
⇒ 1 = 0.80 + 0.80x/100
⇒ 1 - 0.80 = 0.80x/100
⇒ 0.20 = 0.80x/100
⇒ x = (0.20 × 100) / 0.80
⇒ x = 25%
The householder must increase her consumption of sugar by 25% to keep the expenditure unchanged.
Last updated on Jun 16, 2025
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