The price of rice is reduced by 2%. How many kilograms of rice can now be bought for the money which was sufficient to buy 49 kg of rice earlier?

### Concept & Logic When total expenditure remains constant, the quantity purchased is inversely proportional to the price. $$ \text{Price} \times \text{Quantity} = \text{Constant Expenditure} $$ ### Step-by-Step Solution * **Given:** Initial quantity = $49$ kg. Price reduction = $2\%$. * **Calculation:** Let the initial price of rice be $P$ per kg. Initial total expenditure = $49 \times P = 49P$ New price after $2\%$ reduction = $98\%$ of $P = 0.98P$ New quantity is found by dividing the constant expenditure by the new price: New quantity = $\frac{\text{Total Expenditure}}{\text{New Price}}$ New quantity = $\frac{49P}{0.98P}$ The $P$ cancels out: New quantity = $\frac{49}{0.98} = \frac{4900}{98} = 50$ kg. ### Exam Strategy & Shortcut Use the ratio method for lightning-fast solving. A $2\%$ reduction means the price ratio (Old : New) is $100 : 98$, which simplifies to $50 : 49$. Since expenditure is constant, the quantity ratio is the exact inverse of the price ratio. Quantity ratio (Old : New) = $49 : 50$. Since the old quantity is given as exactly $49$ kg, the new quantity corresponds directly to the ratio value of $50$ kg. ### Common Pitfall Students often attempt to calculate $2\%$ of $49$ kg and add it to the original amount. This is mathematically incorrect because the $2\%$ change applies linearly to the *price*, not directly to the *quantity*. Always invert the price ratio to find the quantity change! ### Final Answer Therefore, the correct answer is **50 kg**.