A reduction of 21% in the price of wheat enables a person to buy 10.5 kg more for ₹ 100. What is the reduced price per kg?

### Concept & Strategy The total money saved due to the price reduction is exactly the amount used to purchase the extra quantity at the new (reduced) rate. ### Step-by-Step Solution * **Given:** Price reduction = $21\%$, Extra quantity = $10.5$ kg, Total amount spent = ₹ $100$. * **Calculation:** Money saved due to the $21\%$ reduction = $21\%$ of $100$ Saved Money = $\frac{21}{100} \times 100 = $ ₹ $21$. This saved amount (₹ $21$) is precisely what allows the person to buy the extra $10.5$ kg of wheat at the current, reduced price. Reduced price per kg = $\frac{\text{Saved Money}}{\text{Extra Quantity}}$ Reduced price per kg = $\frac{21}{10.5}$ Reduced price per kg = ₹ $2$. ### Exam Strategy & Shortcut For finding the *reduced/new* price directly, you can memorize and apply this one-step formula: $$ \text{New Price} = \frac{\text{Percentage Change} \times \text{Total Amount}}{100 \times \text{Extra Quantity}} $$ $$ \text{New Price} = \frac{21 \times 100}{100 \times 10.5} = \frac{2100}{1050} = 2 $$ ### Common Pitfall Finding the original price instead of the reduced price. If the question asked for the original price, you would need to divide the new price by $(1 - 0.21)$, i.e., $\frac{2}{0.79}$. This is a common follow-up question, so always double-check which price the examiner is demanding! ### Final Answer Therefore, the correct answer is **₹ 2**.