Profit percentage earned by selling an article for Rs.1920 is equal to the loss percentage when the article is
sold for Rs.1280. At what price should it be sold, if the profit is to be 30%?

Let's solve the problem step by step.

Let the cost price of the article be \( C \).

### Step 1: Establish equations for profit and loss percentages
- When the article is sold for Rs. 1920, there is a profit. Let the profit percentage be \( p \).
- When the article is sold for Rs. 1280, there is a loss. Let the loss percentage be \( p \).

Since the profit percentage when sold at Rs. 1920 is equal to the loss percentage when sold at Rs. 1280, we can write:

\[
\frac{1920 - C}{C} \times 100 = \frac{C - 1280}{C} \times 100
\]

Simplifying, we have:

\[
1920 - C = C - 1280
\]

### Step 2: Solve for the cost price \( C \)
Add \( C \) to both sides:

\[
1920 + 1280 = 2C
\]

\[
C = \frac{3200}{2} = 1600
\]

So, the cost price \( C \) is Rs. 1600.

### Step 3: Find the selling price for a 30% profit
If the profit is to be 30%, the selling price \( S \) should be:

\[
S = C + \frac{30}{100} \times C
\]

\[
S = 1600 + \frac{30}{100} \times 1600
\]

\[
S = 1600 + 480 = 2080
\]

### Final Answer:
The article should be sold for **Rs. 2080** to achieve a 30% profit.

Would you like more details on this solution or have any other questions?

---

Here are 5 related questions for further practice:

1. What would be the profit or loss percentage if the article is sold for Rs. 2000?
2. If the cost price was Rs. 1500, what selling price would result in a 25% profit?
3. Calculate the cost price if selling at Rs. 1800 results in a 20% profit.
4. Determine the selling price for a 40% profit if the article's cost price is Rs. 1800.
5. If the selling price is Rs. 2200, what is the profit percentage?

**Tip:** Understanding the relationship between cost price, selling price, and profit/loss percentage is crucial for solving such problems efficiently.

Learn how to calculate the selling price to achieve a 30% profit using the given cost price, profit, and loss percentages. Detailed step-by-step solution included. Practice related problems and improve your understanding of profit and loss calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation