When a shopkeeper reduces the selling price from 1080 to 1026 its loss increases by 4 percentage point. What is the selling price of this same article when it fetches a profit of 4% ?

Options

A. Rs. 1392
B. Rs. 1404
C. Rs. 1450
D. Rs. 1350

Answer

To solve the problem step by step, we will follow the logical deductions based on the information provided.

### Step 1: Determine the loss and cost price.
Let the cost price (CP) be \( x \).

When the selling price (SP) is reduced from 1080 to 1026, the loss increases by 4 percentage points.

The loss when the SP is 1080 can be expressed as:
\[ \text{Loss} = \text{CP} - \text{SP} = x - 1080 \]

The loss when the SP is 1026 can be expressed as:
\[ \text{Loss} = x - 1026 \]

According to the problem, the difference in loss is equal to 4% of the cost price:
\[ (x - 1026) - (x - 1080) = 0.04x \]

### Step 2: Set up the equation.
Simplifying the left side:
\[ 1080 - 1026 = 0.04x \]
\[ 54 = 0.04x \]

### Step 3: Solve for the cost price.
To find \( x \), we rearrange the equation:
\[ x = \frac{54}{0.04} \]
Calculating this gives:
\[ x = 1350 \]

### Step 4: Calculate the selling price for a profit of 4%.
Now, we need to find the selling price when there is a profit of 4%. The selling price (SP) when there is a profit of 4% can be calculated as:
\[ \text{SP} = \text{CP} + \text{Profit} = CP + 0.04 \times CP = 1.04 \times CP \]
Substituting the cost price:
\[ \text{SP} = 1.04 \times 1350 \]

### Step 5: Calculate the final selling price.
Calculating this gives:
\[ \text{SP} = 1404 \]

Thus, the selling price of the article when it fetches a profit of 4% is **1404**.

### Summary of Steps:
1. Set up the equations based on the loss and selling prices.
2. Solve for the cost price using the relationship between losses.
3. Calculate the selling price for a profit of 4% using the cost price.