The marked price of an electric iron is Rs. 450. The shopkeeper allows a discount of 10% and gains 8%. If no discount is allowed, his gain percent would be

Options

A. (a) 10%
B. (b) 20%
C. (c) 25%
D. (d) 30%

Answer

To solve the problem step by step, we will follow the calculations as outlined in the video transcript.

**Step 1: Calculate the Selling Price (SP) after Discount**
- The marked price (MP) of the electric iron is Rs. 450.
- The discount given is 10% of the marked price.

\[ \text{Discount} = \frac{10}{100} \times 450 = 45 \]

- Now, we subtract the discount from the marked price to find the selling price:

\[ \text{Selling Price (SP)} = \text{Marked Price (MP)} - \text{Discount} = 450 - 45 = 405 \]

**Step 2: Calculate the Cost Price (CP) using the Gain Percentage**
- The gain percentage is given as 8%. We can use the formula for cost price based on selling price and gain percentage:

\[ \text{CP} = \frac{\text{SP} \times 100}{100 + \text{Gain Percentage}} = \frac{405 \times 100}{100 + 8} \]

- Now, calculate the CP:

\[ \text{CP} = \frac{405 \times 100}{108} = \frac{40500}{108} = 375 \]

**Step 3: Calculate the Profit if No Discount is Allowed**
- If no discount is given, the selling price will be equal to the marked price, which is Rs. 450.

- Now, we can calculate the profit:

\[ \text{Profit} = \text{Selling Price (no discount)} - \text{Cost Price (CP)} = 450 - 375 = 75 \]

**Step 4: Calculate the Profit Percentage**
- Finally, we can calculate the profit percentage using the formula:

\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 = \left(\frac{75}{375}\right) \times 100 \]

- Now, simplify the calculation:

\[ \text{Profit Percentage} = \frac{7500}{375} = 20\% \]

Thus, if no discount is allowed, the gain percentage would be **20%**.

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