The cost price of an article is ₹ 7840. What should be the selling price of the article so that there is a profit of 7%? (R.R.B., 2008)

### Concept & Calculating Selling Price When the Cost Price (CP) and the desired profit percentage are given, the Selling Price (SP) can be calculated by applying the percentage increase directly to the Cost Price. $$ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit \%}}{100}\right) $$ ### Step-by-Step Solution Given: * Cost Price (CP) = ₹ 7840 * Desired Profit = 7% Calculation: 1. We need to find 107% of the cost price to determine the total selling price. $$ \text{SP} = 7840 \times \left( \frac{100 + 7}{100} \right) $$ $$ \text{SP} = 7840 \times 1.07 $$ 2. Break down the multiplication for easier calculation: $7840 \times (1 + 0.07)$. $$ \text{SP} = 7840 + (7840 \times 0.07) $$ 3. Calculate 7% of 7840. $$ 7840 \times \frac{7}{100} = 78.4 \times 7 = 548.8 $$ 4. Add the profit back to the CP. $$ \text{SP} = 7840 + 548.8 = 8388.8 $$ ### Exam Strategy & Shortcut Use the **Unit Digit Concept** to save time. When calculating $7840 \times 107 / 100$, ignore the zeroes momentarily and multiply $784 \times 107$. The unit digit of $4 \times 7$ is $8$. After adjusting decimal places, the final digit before the trailing zeroes must be an 8. Looking at the options, only ₹ 8388.80 has an 8 in that significant decimal position. ### Common Pitfall A common mistake is adding the flat value of 7 to the price or calculating 7% incorrectly due to decimal placement errors (e.g., adding 54.88 instead of 548.8). Always double-check decimal shifts. ### Final Answer Therefore, the correct answer is **₹ 8388.80**.