Question

A shopkeeper bought a bag for Rs 1200 and sold it at a profit of 15%. Find the selling price.

• A. Rs 1320
• B. Rs 1360
• C. Rs 1380
• D. Rs 1400

Hint:

To find 15% of any number mentally:
First, find 10% of the number (just divide by 10, e.g., 10% of 1200 = 120).
Then, find 5% of the number (half of the 10% value, e.g., 60).
Add them together: 120 + 60 = 180. This is 15% of the number.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This is a standard profit and loss arithmetic problem where we are given the Cost Price (CP) of an item and the Profit Percentage. We need to find the final Selling Price (SP).

Step 2: Key Formula or Approach:
• We can use either the absolute profit method or the direct percentage multiplier method.
- Method 1: Find the absolute profit and add it to the Cost Price.
\[ \text{Profit Amount} = \frac{\text{Profit Percentage}}{100} \times \text{CP} \] \[ \text{SP} = \text{CP} + \text{Profit Amount} \] - Method 2: Apply the direct multiplier formula.
\[ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]

Step 3: Detailed Explanation:

• 1. Identify the values provided in the problem statement:
- Cost Price (CP) = Rs 1200
- Profit Percentage = 15%

• 2. Let us compute the solution using Method 1:
- Calculate the profit amount: \[ \text{Profit Amount} = \frac{15}{100} \times 1200 \] - Simplify the expression: \[ \text{Profit Amount} = 15 \times 12 = 180 \] - So, the profit earned by the shopkeeper is Rs 180.
- Now, determine the Selling Price (SP) by adding the profit to the Cost Price: \[ \text{SP} = 1200 + 180 = 1380 \]
• 3. Let us verify using Method 2 (Direct Multiplier):
- A profit of 15% means the Selling Price is 115% of the Cost Price. \[ \text{SP} = 115% \text{ of } 1200 \] \[ \text{SP} = \frac{115}{100} \times 1200 \] - Simplify the expression: \[ \text{SP} = 115 \times 12 \] - Compute the multiplication: \[ 115 \times 12 = 1380 \] - Both methods yield the exact same result of Rs 1380.

Step 4: Final Answer:
The selling price of the bag is Rs 1380. Hence, the correct option is (C).