Understanding the Shopkeeper's Transaction and Profit

This problem involves calculating the profit percentage earned by a shopkeeper on the sale of an article. To find the profit percentage, we need to determine the cost price (CP) for the shopkeeper and the final selling price (SP) at which the article is sold to the customer after applying discounts.

Here's a breakdown of the information given:

• Cost Price (CP) for the shopkeeper: Rs. 4,000
• Marked Price (MP) of the article: Rs. 8,400
• First Discount: 25% on the Marked Price
• Second Discount: 15% on the price after the first discount (if a coupon is redeemed)

The question asks for the profit percentage in the transaction where the customer redeems the coupon, meaning both discounts are applied.

Step-by-Step Calculation of the Selling Price

First, let's calculate the price after the first discount of 25% on the Marked Price.

Marked Price (MP) = Rs. 8,400

First Discount amount = 25% of MP

First Discount amount = $\frac{25}{100} \times 8400 = 0.25 \times 8400$

First Discount amount = Rs. 2,100

Price after first discount = MP - First Discount amount

Price after first discount = $8400 - 2100$

Price after first discount = Rs. 6,300

Now, the customer gets a further discount of 15% on this discounted price (Rs. 6,300) by redeeming a coupon. This will be the final selling price (SP).

Second Discount amount = 15% of the price after the first discount

Second Discount amount = 15% of 6300

Second Discount amount = $\frac{15}{100} \times 6300 = 0.15 \times 6300$

Second Discount amount = Rs. 945

Final Selling Price (SP) = Price after first discount - Second Discount amount

Final Selling Price (SP) = $6300 - 945$

Final Selling Price (SP) = Rs. 5,355

Calculating the Profit and Profit Percentage

Now that we have the Cost Price (CP) and the Selling Price (SP), we can calculate the Profit earned by the shopkeeper.

Cost Price (CP) = Rs. 4,000

Selling Price (SP) = Rs. 5,355

Profit = SP - CP

Profit = $5355 - 4000$

Profit = Rs. 1,355

Finally, we calculate the Profit Percentage.

Profit Percentage = $\left( \frac{\text{Profit}}{\text{CP}} \right) \times 100$

Profit Percentage = $\left( \frac{1355}{4000} \right) \times 100$

Profit Percentage = $\frac{1355}{40}$

Profit Percentage = $33.875\%$

The question asks for the profit percentage to the nearest integer.

Rounding $33.875\%$ to the nearest integer gives $34\%$.

Conclusion on Shopkeeper's Profit Percentage

The profit percentage earned by the shopkeeper in this transaction, after applying both discounts, is approximately 34% when rounded to the nearest integer.

Revision Table: Key Concepts in Profit and Loss

Additional Information: Understanding Successive Discounts

Successive discounts are multiple discounts applied one after another on a price. When two successive discounts, say $d_1\%$ and $d_2\%$, are applied, the second discount is calculated not on the original price, but on the price after the first discount has been applied.

The net discount percentage equivalent to two successive discounts of $d_1\%$ and $d_2\%$ is not simply $d_1 + d_2$. The equivalent single discount percentage can be calculated using the formula:

Equivalent Discount % = $\left( d_1 + d_2 - \frac{d_1 \times d_2}{100} \right)\%$

In this problem, the discounts were 25% and 15%. Let's calculate the equivalent single discount on the Marked Price:

Equivalent Discount % = $\left( 25 + 15 - \frac{25 \times 15}{100} \right)\%$

Equivalent Discount % = $\left( 40 - \frac{375}{100} \right)\%$

Equivalent Discount % = $(40 - 3.75)\%$

Equivalent Discount % = $36.25\%$

This means the article was sold at a net discount of 36.25% on the Marked Price (Rs. 8,400).

Let's verify the Selling Price using this equivalent discount:

Selling Price = MP - (Equivalent Discount % of MP)

Selling Price = $8400 - \left( \frac{36.25}{100} \times 8400 \right)$

Selling Price = $8400 - (0.3625 \times 8400)$

Selling Price = $8400 - 3045$

Selling Price = Rs. 5,355

This matches the selling price calculated earlier, confirming the understanding of successive discounts. The profit calculation then follows from this selling price and the original cost price.