When an article is sold for ₹ 703 loss incurred is`25%` less than the profit earned on selling it at ₹ 836. What is the selling price of the article when it earns a profit of `20%`?

Options

A. 912
B. 1576
C. 1532
D. 1092

Answer

To solve the problem step by step, let's denote the following:

- Let the Cost Price (CP) of the article be \( x \).
- The Selling Price (SP) when sold for a loss is ₹ 703.
- The Selling Price (SP) when sold for a profit is ₹ 836.

### Step 1: Calculate the Loss and Profit
When the article is sold for ₹ 703, it incurs a loss. The loss can be calculated as:
\[ \text{Loss} = \text{CP} - \text{SP} = x - 703 \]

When the article is sold for ₹ 836, it earns a profit. The profit can be calculated as:
\[ \text{Profit} = \text{SP} - \text{CP} = 836 - x \]

### Step 2: Relate Loss and Profit
According to the problem, the loss incurred (when sold for ₹ 703) is 25% less than the profit earned (when sold for ₹ 836). This can be expressed mathematically as:
\[ x - 703 = (836 - x) - 0.25(836 - x) \]

### Step 3: Simplify the Equation
Now, let's simplify the right side of the equation:
\[ x - 703 = (836 - x) - 0.25(836 - x) \]
\[ x - 703 = (836 - x) \times (1 - 0.25) \]
\[ x - 703 = (836 - x) \times 0.75 \]
\[ x - 703 = 0.75 \times 836 - 0.75x \]
\[ x - 703 = 627 - 0.75x \]

### Step 4: Rearranging the Equation
Now, let's rearrange the equation to isolate \( x \):
\[ x + 0.75x = 627 + 703 \]
\[ 1.75x = 1330 \]
\[ x = \frac{1330}{1.75} \]
\[ x = 760 \]

### Step 5: Calculate the Selling Price for 20% Profit
Now that we have the Cost Price (CP) as ₹ 760, we can find the Selling Price (SP) when there is a profit of 20%. The formula for Selling Price with profit is:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where Profit can be calculated as:
\[ \text{Profit} = 20\% \text{ of CP} = \frac{20}{100} \times 760 = 152 \]
Thus,
\[ \text{SP} = 760 + 152 = 912 \]

### Final Answer
The selling price of the article when it earns a profit of 20% is ₹ 912.

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