A merchant bought an article after getting 35% discount on its MRP. Merchant marks it Rs600 more than the price he had bought and gives a discount of 15%-on it. If amount of profit earn by merchant is Rs432, then find the initial marked for merchant.

Options

A. Rs. 600
B. Rs. 800
C. Rs. 1000
D. Rs. 750

Answer

To solve the problem step by step, we will break down the information provided and use algebra to find the initial marked price (MRP) for the merchant.

### Step 1: Define the MRP
Let the MRP (Marked Price) be represented as \( M \).

### Step 2: Calculate the Cost Price
The merchant bought the article at a 35% discount on the MRP. Therefore, the cost price (CP) can be calculated as:
\[ CP = M \times \left(1 - \frac{35}{100}\right) = M \times \frac{65}{100} = 0.65M \]

### Step 3: Determine the Marked Price
The merchant marks the article at Rs. 600 more than the cost price. Thus, the marked price (MP) is:
\[ MP = CP + 600 = 0.65M + 600 \]

### Step 4: Calculate the Selling Price
The merchant gives a discount of 15% on the marked price. The selling price (SP) can be expressed as:
\[ SP = MP \times \left(1 - \frac{15}{100}\right) = MP \times \frac{85}{100} \]
Substituting the value of MP from Step 3:
\[ SP = (0.65M + 600) \times \frac{85}{100} \]

### Step 5: Set Up the Profit Equation
The profit earned by the merchant is given as Rs. 432. Profit is calculated as:
\[ Profit = SP - CP \]
Substituting the values of SP and CP:
\[ 432 = \left((0.65M + 600) \times \frac{85}{100}\right) - 0.65M \]

### Step 6: Simplify the Equation
Now, we will simplify the equation:
\[ 432 = \left(0.85 \times 0.65M + 600 \times 0.85\right) - 0.65M \]
Calculating \( 600 \times 0.85 \):
\[ 600 \times 0.85 = 510 \]
So the equation becomes:
\[ 432 = (0.5525M + 510) - 0.65M \]
Combining like terms:
\[ 432 = 510 - 0.0975M \]

### Step 7: Rearranging the Equation
Rearranging gives:
\[ 0.0975M = 510 - 432 \]
Calculating the right side:
\[ 0.0975M = 78 \]

### Step 8: Solve for M
Now, divide both sides by 0.0975 to find M:
\[ M = \frac{78}{0.0975} \approx 800 \]

### Conclusion
Thus, the initial marked price (MRP) for the merchant is:
\[ \text{MRP} = 800 \text{ Rs.} \]