The difference between the sell ing price and cost price of an article is Rs 210. If the profit per cent is 25, then the selling price of the article is

Options

A. 950
B. 1050
C. 1150
D. 1250

Answer

To solve the problem step by step, we need to find the selling price (SP) of an article given the profit percentage and the difference between the selling price and cost price (CP).

### Step 1: Understand the Given Information
We know:
- The difference between the selling price (SP) and cost price (CP) is Rs 210.
- The profit percentage is 25%.

### Step 2: Express Profit Percentage as a Fraction
The profit percentage of 25% can be expressed as a fraction:
\[ \text{Profit} = \frac{25}{100} = \frac{1}{4} \]
This means for every 4 parts of the cost price, there is 1 part of profit.

### Step 3: Calculate the Selling Price and Cost Price Relationship
From the profit percentage, we can say:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]
Since the profit is \(\frac{1}{4}\) of the cost price, we can write:
\[ \text{Profit} = \frac{1}{4} \times \text{CP} \]
Thus,
\[ \text{SP} = \text{CP} + \frac{1}{4} \text{CP} = \frac{5}{4} \text{CP} \]

### Step 4: Set Up the Equation Using the Given Difference
According to the problem, the difference between SP and CP is Rs 210:
\[ \text{SP} - \text{CP} = 210 \]
Substituting the expression for SP:
\[ \frac{5}{4} \text{CP} - \text{CP} = 210 \]
This simplifies to:
\[ \frac{5}{4} \text{CP} - \frac{4}{4} \text{CP} = 210 \]
\[ \frac{1}{4} \text{CP} = 210 \]

### Step 5: Solve for Cost Price (CP)
To find CP, multiply both sides by 4:
\[ \text{CP} = 210 \times 4 = 840 \]

### Step 6: Calculate Selling Price (SP)
Now that we have CP, we can find SP:
\[ \text{SP} = \frac{5}{4} \text{CP} = \frac{5}{4} \times 840 = 1050 \]

### Conclusion
The selling price of the article is Rs 1050.