Question : If the price of rice is increased by 25 percent, then by what percentage consumption of rice should be decreased so that the expenditure incurred on rice gets decreased by 40 percent?
Option 1: 52 percent
Option 2: 43.33 percent
Option 3: 42 percent
Option 4: 48 percent
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Correct Answer: 52 percent
Solution :
Increase in price = 25%
Decrease in expenditure = 40%
(Initial price × Initial consumption) = (Final price × Final consumption)
Let's denote the initial price and consumption as P and C, and the final price and consumption as P' and C'.
Initial expenditure = P × C
Final expenditure = P' × C' = (P × 1.25) × C'
Also according to the question, final expenditure = 0.6 × P × C
⇒ (P × 1.25) × C' = 0.6 × P × C
⇒ $\frac{C'}{C}$ = $\frac{0.6}{1.25}$ = 0.48
⇒ This represents a decrease in consumption by 1 – 0.48 = 0.52 or 52%.
Therefore, the consumption of rice should be decreased by 52% to decrease the expenditure by 40%.
Hence, the correct answer is 52%.
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