Rajeev buys goods worth ₹ 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.

### Concept & Logic When both a discount (rebate) and a tax are applied, they must be calculated sequentially, not simultaneously. The rebate decreases the initial cost, and the sales tax is then applied to that newly reduced amount. $$ \text{Final Amount} = \text{Initial Price} \times \left(1 - \frac{\text{Rebate}}{100}\right) \times \left(1 + \frac{\text{Tax}}{100}\right) $$ ### Step-by-Step Solution * **Given:** Initial value of goods = ₹ 6650 Rebate (Discount) = 6% Sales Tax = 10% * **Calculation:** Step 1: Calculate the amount after the 6% rebate. Price after rebate = $ 6650 \times \left(1 - 0.06\right) = 6650 \times 0.94 $ Price after rebate = ₹ 6251 Step 2: Calculate the final amount by adding the 10% sales tax to the rebated price. Final Amount = $ 6251 \times \left(1 + 0.10\right) = 6251 \times 1.10 $ Final Amount = ₹ 6876.10 ### Exam Strategy & Shortcut Use successive percentage multipliers to solve it in a single line. Final Price = $ 6650 \times 0.94 \times 1.10 $. Instead of multiplying 0.94 by 6650 first, multiply $ 0.94 \times 1.10 = 1.034 $. Now, calculate $ 6650 \times 1.034 $. To do this mentally: $ 6650 \times 1 = 6650 $. Plus 3% of 6650 ($ 199.5 $) plus 0.4% ($ 26.6 $). $ 6650 + 199.5 + 26.6 = 6876.10 $. ### Common Pitfall A major mistake is combining the percentages by simply taking the net difference (e.g., $ 10\% \text{ tax} - 6\% \text{ rebate} = +4\% $). Applying a flat 4% increase to ₹ 6650 yields ₹ 6916, which is incorrect because the base amount changes after the rebate. ### Final Answer **Therefore, the correct answer is ₹ 6876.10.**