If an article with marked price of ₹ $400$ is sold at successive discounts of $10\%$, $25\%$ and $15\%$, what is the approximate price the customer has to pay? (Campus Recruitment, 2009)

### Concept & Strategy When faced with multiple successive discounts, sequentially apply each discount multiplier to the original marked price to find the final selling price. Since the question asks for an approximate value, minor rounding at the final step is expected. $$ \text{Final Price} = \text{MP} \times \left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right) \times \left(1 - \frac{d_3}{100}\right) $$ ### Step-by-Step Solution * **Given:** * Marked Price = ₹ $400$ * First discount = $10\%$ * Second discount = $25\%$ * Third discount = $15\%$ * **Calculation:** * Apply the first discount of $10\%$: $400 \times 0.90 = ₹ 360$. * Apply the second discount of $25\%$ on ₹ $360$: $25\%$ is $\frac{1}{4}$. $\frac{1}{4}$ of $360$ is $90$. $360 - 90 = ₹ 270$. * Apply the third discount of $15\%$ on ₹ $270$: $15\%$ of $270 = \frac{15 \times 270}{100} = \frac{4050}{100} = 40.50$. Final Price = $270 - 40.50 = ₹ 229.50$. * The approximate value is ₹ $230$. ### Exam Strategy & Shortcut Convert the percentages into simple fraction multipliers: $10\%$ off $\rightarrow$ multiply by $\frac{9}{10}$ $25\%$ off $\rightarrow$ multiply by $\frac{3}{4}$ $15\%$ off $\rightarrow$ multiply by $\frac{17}{20}$ $\text{Price} = 400 \times \frac{9}{10} \times \frac{3}{4} \times \frac{17}{20}$ $= 400 \times \frac{459}{800} = \frac{459}{2} = 229.5$. Approximating this yields $230$, making fraction multiplication very efficient. ### Common Pitfall Summing the discounts to $50\%$ and calculating half of $400$ to get $200$. Successive discounts always yield a smaller total reduction than their direct sum. ### Final Answer Therefore, the correct answer is **₹ 230**.