Applied to a bill for ₹ $1,00,000$, the difference between a discount of $40\%$ and two successive discounts of $36\%$ and $4\%$ is

### Concept & Logic The difference between a single discount $(x + y)\%$ and two successive discounts of $x\%$ and $y\%$ is exactly the interaction term $\frac{x \times y}{100}\%$. $$ \text{Difference \%} = \frac{x \times y}{100}\% $$ ### Step-by-Step Solution * **Given:** * Bill amount = ₹ $1,00,000$ * Single discount = $40\%$ * Successive discounts = $36\%$ and $4\%$ * **Calculation:** * Equivalent discount for $36\%$ and $4\%$ = $36 + 4 - \frac{36 \times 4}{100} = 40 - 1.44 = 38.56\%$. * Difference in discount percentage = $40\% - 38.56\% = 1.44\%$. * Calculate the actual monetary difference: $1.44\%$ of $1,00,000 = \frac{1.44}{100} \times 100000 = 1440$. ### Exam Strategy & Shortcut Bypass calculating the full equivalent discount. Since the single discount $40\%$ is the exact sum of $36\%$ and $4\%$, the difference is simply the product divided by $100$: $\frac{36 \times 4}{100} = 1.44\%$. Directly compute $1.44\%$ of ₹ $1,00,000$ to get $1440$. ### Common Pitfall Assuming that a single discount of $40\%$ is equal to successive discounts of $36\%$ and $4\%$, which would lead to choosing "Nil". ### Final Answer Therefore, the correct answer is **₹ 1440**.