Question : The price of rice is decreased by 25% and therefore a person can purchase 30 kg more rice in the same expenditure. If the expenditure is INR 5,400, then what was the original price of rice per kg?
Option 1: INR 90 per kg
Option 2: INR 60 per kg
Option 3: INR 75 per kg
Option 4: INR 50 per kg
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Correct Answer: INR 60 per kg
Solution : Given: The price of rice is decreased by 25% and therefore a person can purchase 30 kg more rice in the same expenditure. The expenditure is INR 5,400. We know the formula, Expenditure = Price × Quantity. Let $x$ and $y$ be the previous price and amount of rice purchased, respectively. $xy=0.75x\times(y+30)$ ⇒ $xy=0.75xy+22.5x$ ⇒ $0.25xy=22.5x$ ⇒ $y=90$ kg The original price of rice per kg = $\frac{5400}{90}$ = INR 60 per kg. Hence, the correct answer is INR 60 per kg.
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