Ramesh marks his goods 30% above cost price. If he sells the item for 910 after allowing a discount of 15%, find his cost price.

Options

A. Rs. 823.5
B. Rs. 758
C. Rs. 814.2
D. Rs. 856.5

Answer

To solve the problem step by step, we will follow the given information and use the formulas related to cost price, marked price, and selling price.

### Step 1: Define the Cost Price (CP)
Let the cost price of the item be \( CP \).

### Step 2: Calculate the Marked Price (MP)
Ramesh marks his goods 30% above the cost price. Therefore, the marked price can be calculated as:
\[ MP = CP + 30\% \text{ of } CP = CP + 0.30 \times CP = 1.30 \times CP \]

### Step 3: Determine the Selling Price (SP)
Ramesh sells the item for ₹910 after allowing a discount of 15%. The selling price can be calculated using the formula for selling price after discount:
\[ SP = MP - \text{Discount} \]
The discount is 15% of the marked price:
\[ \text{Discount} = 15\% \text{ of } MP = 0.15 \times MP \]
Thus, we can express the selling price as:
\[ SP = MP - 0.15 \times MP = (1 - 0.15) \times MP = 0.85 \times MP \]

### Step 4: Set up the equation
Since we know that the selling price is ₹910, we can set up the equation:
\[ 0.85 \times MP = 910 \]

### Step 5: Substitute the Marked Price in the equation
Now, substitute the expression for \( MP \) from Step 2 into the equation:
\[ 0.85 \times (1.30 \times CP) = 910 \]

### Step 6: Simplify the equation
Now simplify the equation:
\[ 1.105 \times CP = 910 \]

### Step 7: Solve for the Cost Price (CP)
To find \( CP \), divide both sides by 1.105:
\[ CP = \frac{910}{1.105} \]
Calculating this gives:
\[ CP \approx 824.78 \]

### Step 8: Round to two decimal places
Thus, the cost price of the item is approximately ₹824.78.

### Final Answer
The cost price of the item is ₹824.78.

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