Step 1: Understanding the Question:
This problem falls under the mathematical topic of Commercial Arithmetic, specifically Profit and Loss involving Markup and Discounts. The objective is to determine the final Selling Price (SP) of an item by navigating through two pricing stages: the first is the transition from Cost Price (CP) to Marked Price (MP) via a markup, and the second is the transition from Marked Price to Selling Price via a percentage reduction known as a discount. We are provided with a starting capital amount of Rs 800 and two distinct percentage modifiers that must be applied sequentially.
Step 2 : Key Formulas and approach:
To solve this, we utilize the sequential relationship between the three price types:
1. Marked Price Formula: $\text{MP} = \text{CP} \times \left(1 + \frac{\text{Markup %}}{100}\right)$
2. Selling Price Formula: $\text{SP} = \text{MP} \times \left(1 - \frac{\text{Discount %}}{100}\right)$
The approach involves a step-by-step calculation where the result of the markup becomes the base for the discount calculation.
Step 3 : Detailed Explanation:
We begin by identifying the initial investment or Cost Price (CP) given as Rs 800. The shopkeeper intends to raise the price to create a profit margin, so he marks it up by 25%.
To find the amount added to the CP, we calculate 25% of 800. Since 25% is equivalent to one-fourth, we divide 800 by 4, which yields Rs 200. Alternatively, $\frac{25}{100} \times 800 = 200$.
The first milestone is the Marked Price (MP). By adding the markup amount to the original cost, we get $\text{MP} = 800 + 200 = Rs 1000$. This is the price displayed on the tag before any negotiations or sales.
Next, we address the consumer incentive, which is a 10% discount. It is crucial to remember that a discount is always calculated on the Marked Price, not the Cost Price. We calculate 10% of our new base, which is Rs 1000.
The discount amount is determined as $\frac{10}{100} \times 1000 = Rs 100$. This represents the reduction in price offered to the buyer from the tag price.
Finally, we derive the Selling Price (SP) by subtracting this discount from the Marked Price. So, $\text{SP} = 1000 - 100 = Rs 900$.
This confirms that even after a 10% discount, the shopkeeper sells the item for Rs 100 more than the original cost, representing a profit of Rs 100.
Step 4 : Final Answer:
The final selling price of the article after the markup and discount is Rs 900, which corresponds to option (B).