The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 50% profit ?

Options

A. a. 960
B. b. 1000
C. c. 1060
D. d. 525

Explanation

To solve the problem, we need to find the cost price (CP) of the article first, and then determine the selling price (SP) that would yield a 50% profit.

### Step 1: Understand the relationship between selling price, profit, and loss.

We know that:
- Selling Price (SP1) = Rs. 832 (where profit is earned)
- Selling Price (SP2) = Rs. 448 (where loss is incurred)

According to the problem, the profit from selling at Rs. 832 is equal to the loss from selling at Rs. 448.

### Step 2: Set up the equations.

Let the Cost Price (CP) of the article be Rs. x.

- Profit when sold for Rs. 832:
\[ \text{Profit} = SP1 - CP = 832 - x \]

- Loss when sold for Rs. 448:
\[ \text{Loss} = CP - SP2 = x - 448 \]

### Step 3: Equate profit and loss.

Since the profit is equal to the loss:
\[ 832 - x = x - 448 \]

### Step 4: Solve for x.

Now, we can solve the equation:
\[ 832 + 448 = 2x \]
\[ 1280 = 2x \]
\[ x = \frac{1280}{2} = 640 \]

So, the Cost Price (CP) of the article is Rs. 640.

### Step 5: Calculate the selling price for a 50% profit.

To find the selling price for a 50% profit, we use the formula:
\[ \text{Selling Price (SP)} = CP + \text{Profit} \]
Where Profit = 50% of CP:
\[ \text{Profit} = 0.5 \times CP = 0.5 \times 640 = 320 \]

Now, we can find the selling price:
\[ SP = CP + \text{Profit} = 640 + 320 = 960 \]

### Final Answer:
The selling price for making a 50% profit should be Rs. 960.

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