The MP of an article is Rs. 4370. after allowing u% discount a shopkeeper still gains v%. If no discount is allowed then he gain `35 ( 5)/(7)%`. Find the CP of article?

Options

A. Rs. 3450
B. Rs. 3024
C. Rs. 2940
D. Rs. 3220

Answer

To find the cost price (CP) of the article given the mark price (MP) and profit percentages, we can follow these steps:

### Given:
- Mark Price (MP) = Rs. 4370
- Profit Percentage when no discount is allowed = \( 35 \frac{5}{7} \% \)

### Step 1: Convert the profit percentage into a fraction
The profit percentage \( 35 \frac{5}{7} \% \) can be converted into an improper fraction:
\[ 35 \frac{5}{7} = \frac{35 \times 7 + 5}{7} = \frac{245 + 5}{7} = \frac{250}{7} \% \]

### Step 2: Use the formula for Selling Price (SP)
When no discount is allowed, the Selling Price (SP) is equal to the Mark Price (MP):
\[ SP = MP = 4370 \]

### Step 3: Relate SP, CP, and Profit Percentage
The relationship between Selling Price, Cost Price, and Profit Percentage is given by:
\[ SP = CP \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]
Substituting the values we have:
\[ 4370 = CP \times \left(1 + \frac{250/7}{100}\right) \]

### Step 4: Simplify the equation
First, convert the profit percentage into decimal form:
\[ 1 + \frac{250/7}{100} = 1 + \frac{250}{700} = 1 + \frac{25}{70} = \frac{70 + 25}{70} = \frac{95}{70} \]
Now substituting this back into the equation:
\[ 4370 = CP \times \frac{95}{70} \]

### Step 5: Solve for CP
Rearranging gives:
\[ CP = 4370 \times \frac{70}{95} \]

### Step 6: Calculate CP
Calculating the right-hand side:
\[ CP = 4370 \times \frac{70}{95} \]
Calculating \( \frac{4370 \times 70}{95} \):
\[ = \frac{305900}{95} = 3220 \]

### Conclusion
The Cost Price (CP) of the article is Rs. 3220.

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