The marked price of a helmet is 30% more than its cost price. If the helmet is sold for Rs. 744 after a discount of Rs. 36, then what will be the profit per cent ?

Options

A. 24
B. 18
C. 21
D. 27

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Selling Price (SP)
The selling price of the helmet is given as Rs. 744.

### Step 2: Calculate the Marked Price (MP)
The helmet is sold after a discount of Rs. 36. Therefore, we can find the marked price using the formula:
\[ \text{MP} = \text{SP} + \text{Discount} \]
\[ \text{MP} = 744 + 36 = 780 \]

### Step 3: Relate the Marked Price to the Cost Price (CP)
We know that the marked price is 30% more than the cost price. This can be expressed as:
\[ \text{MP} = \text{CP} + 0.30 \times \text{CP} \]
\[ \text{MP} = 1.30 \times \text{CP} \]

### Step 4: Substitute the Marked Price into the Equation
Now we can substitute the value of the marked price we found:
\[ 780 = 1.30 \times \text{CP} \]

### Step 5: Solve for the Cost Price (CP)
To find the cost price, we rearrange the equation:
\[ \text{CP} = \frac{780}{1.30} \]
\[ \text{CP} = 600 \]

### Step 6: Calculate the Profit
Profit can be calculated using the formula:
\[ \text{Profit} = \text{SP} - \text{CP} \]
\[ \text{Profit} = 744 - 600 = 144 \]

### Step 7: Calculate the Profit Percentage
Profit percentage is calculated as:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]
\[ \text{Profit Percentage} = \left( \frac{144}{600} \right) \times 100 \]
\[ \text{Profit Percentage} = 24\% \]

### Final Answer
The profit percentage is **24%**.

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