The price of sugar having gone down by 10%, Sharad can buy 6.2 kg more for ₹ 279. The difference between the original and the reduced price (per kg) is

### Concept & Strategy When the price of a commodity decreases, the money saved due to the price drop allows a person to purchase extra quantity at the *new (reduced)* rate. Finding this reduced rate first is the key to unlocking the original price. $$ \text{Reduced Price} = \frac{\text{Money Saved}}{\text{Extra Quantity}} $$ ### Step-by-Step Solution * **Given:** Price drop = $10\%$, Extra quantity = $6.2$ kg, Total amount = ₹ $279$. * **Calculation:** First, calculate the total money saved due to the $10\%$ price reduction. Money Saved = $10\%$ of ₹ $279 = $ ₹ $27.90$ This saved money buys the extra $6.2$ kg of sugar at the current reduced price. Reduced Price per kg = $\frac{27.90}{6.2} = $ ₹ $4.50$ per kg. Next, find the original price. The reduced price is $90\%$ (i.e., $100\% - 10\%$) of the original price. Let original price be $x$. $0.90x = 4.50$ $x = \frac{4.50}{0.90} = $ ₹ $5.00$ per kg. Finally, calculate the difference between the original and reduced prices: Difference = $5.00 - 4.50 = $ ₹ $0.50$. ### Exam Strategy & Shortcut Use ratios to bypass heavy decimals. A $10\%$ drop means the price ratio (Old : New) is $10 : 9$. Because expenditure is constant, the quantity ratio (Old : New) is $9 : 10$. The difference in quantity is $1$ ratio unit, which equals $6.2$ kg. Old quantity = $9 \times 6.2 = 55.8$ kg. Old price = $\frac{279}{55.8} = $ ₹ $5$. New price = $90\%$ of $5 = $ ₹ $4.50$. Difference = $5 - 4.5 = 0.50$. ### Common Pitfall Students often stop at calculating the reduced price (₹ $4.50$) and mistakenly select option (d). The question explicitly asks for the *difference* between the original and reduced price. Always read the final sentence of the prompt twice. ### Final Answer Therefore, the correct answer is **₹ 0.50**.