The price of sugar increases by 15%. By what percentage should the consumption of sugar be decreased so that the expenditure on the purchase of sugar remains the same? [Give your answer correct to 2 decimal places.]
5Q:
The price of sugar increases by 15%. By what percentage should the consumption of sugar be decreased so that the expenditure on the purchase of sugar remains the same? [Give your answer correct to 2 decimal places.]
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Answer : 4. "13.04%"
Explanation :
To solve this problem, let's denote:
- Initial price of sugar = P
- Initial quantity consumed = Q
- Initial expenditure = PQ
After the price increases by 15%, the new price becomes 1.15P.
To keep the expenditure constant, the new quantity consumed (let's call it Q') can be calculated using the formula:
New expenditure = New price × New quantity
Setting the new expenditure equal to the initial expenditure:
PQ = (1.15P) * Q'
Now, solve for Q':
Q' = PQ / (1.15P)
Simplify:
Q' = Q / 1.15
Now, let's find the percentage decrease in consumption:
Percentage decrease = [(Q - Q') / Q] * 100
Substituting the value of Q':
Percentage decrease = [(Q - (Q / 1.15)) / Q] * 100
Percentage decrease = [(Q * (1 - 1/1.15)) / Q] * 100
Percentage decrease ≈ [(1 - 0.8696) * 100] ≈ 13.04%
Therefore, the consumption of sugar should be decreased by approximately 13.04% to keep the expenditure on the purchase of sugar the same after a 15% increase in price.