By selling a bag at Rs. 230, profit of 15% is made. The selling price of the bag, when it is sold at 20% profit would be

Options

A. Rs. 250
B. Rs. 205
C. Rs. 240
D. Rs. 200

Answer

To solve the problem step by step, we need to find the selling price of the bag when it is sold at a 20% profit, given that it is sold at Rs. 230 with a 15% profit.

### Step 1: Understand the relationship between selling price, cost price, and profit percentage.
The selling price (SP) can be calculated using the formula:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where:
- SP = Selling Price
- CP = Cost Price
- Profit = Profit Percentage × CP

### Step 2: Set up the equation for the given situation.
We know that selling the bag at Rs. 230 gives a profit of 15%. Therefore, we can express this as:
\[ 230 = \text{CP} + 0.15 \times \text{CP} \]
This can be rewritten as:
\[ 230 = \text{CP} \times (1 + 0.15) \]
\[ 230 = \text{CP} \times 1.15 \]

### Step 3: Solve for the Cost Price (CP).
To find the cost price, we rearrange the equation:
\[ \text{CP} = \frac{230}{1.15} \]

### Step 4: Calculate the Cost Price.
Now we can perform the calculation:
\[ \text{CP} = \frac{230}{1.15} = 200 \]
So, the cost price of the bag is Rs. 200.

### Step 5: Calculate the Selling Price for a 20% profit.
Now, we need to find the selling price when the profit is 20%. Using the formula for selling price:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where the profit for 20% is:
\[ \text{Profit} = 0.20 \times \text{CP} \]
Thus, the selling price becomes:
\[ \text{SP} = \text{CP} + 0.20 \times \text{CP} \]
\[ \text{SP} = \text{CP} \times (1 + 0.20) \]
\[ \text{SP} = 200 \times 1.20 \]

### Step 6: Calculate the Selling Price.
Now we can perform the calculation:
\[ \text{SP} = 200 \times 1.20 = 240 \]

### Final Answer:
The selling price of the bag when sold at a 20% profit is Rs. 240.

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