The marked price of an electric iron is Rs. 690. The shopkeeper allows a discount of 10% and gains 8%. If no discount is allowed, his gain per cent would be

Options

A. `20%`
B. `24%`
C. `25%`
D. `28%`

Answer

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

### Step 1: Identify the given values
- Marked Price (MP) = Rs. 690
- Discount Percentage (D) = 10%
- Profit Percentage (P) = 8%

### Step 2: Calculate the Selling Price (SP) after the discount
The Selling Price can be calculated using the formula:
\[ SP = MP - (D \% \text{ of } MP) \]
Calculating the discount amount:
\[ D \% \text{ of } MP = \frac{10}{100} \times 690 = 69 \]
Now, calculate the Selling Price:
\[ SP = 690 - 69 = 621 \]

### Step 3: Relate Selling Price to Cost Price
The Selling Price is also related to the Cost Price (CP) using the profit percentage:
\[ SP = CP + (P \% \text{ of } CP) \]
This can be rearranged to:
\[ SP = CP \times \left(1 + \frac{P}{100}\right) \]
Substituting the values:
\[ 621 = CP \times \left(1 + \frac{8}{100}\right) \]
\[ 621 = CP \times 1.08 \]

### Step 4: Calculate the Cost Price (CP)
Now, we can find the Cost Price:
\[ CP = \frac{621}{1.08} \]
Calculating CP:
\[ CP = 575 \]

### Step 5: Calculate the Gain Percentage if no discount is allowed
If no discount is allowed, the Selling Price would be equal to the Marked Price:
\[ SP = MP = 690 \]
Now, we can calculate the profit when no discount is allowed:
\[ \text{Profit} = SP - CP = 690 - 575 = 115 \]

### Step 6: Calculate the Gain Percentage
The Gain Percentage can be calculated using the formula:
\[ \text{Gain \%} = \left(\frac{\text{Profit}}{CP}\right) \times 100 \]
Substituting the values:
\[ \text{Gain \%} = \left(\frac{115}{575}\right) \times 100 \]
Calculating Gain Percentage:
\[ \text{Gain \%} = 20 \]

### Final Answer
If no discount is allowed, the gain percentage would be **20%**.

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