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 the outlined process to find the gain percentage if no discount is allowed.

### Step 1: Calculate the Selling Price after Discount
The marked price (MP) of the electric iron is Rs. 690, and the shopkeeper allows a discount of 10%.

**Formula for Selling Price (SP):**
\[ SP = MP - (Discount \% \times MP) \]

**Calculating Discount:**
\[ Discount = 10\% \times 690 = \frac{10}{100} \times 690 = 69 \]

**Calculating Selling Price:**
\[ SP = 690 - 69 = 621 \]

### Step 2: Calculate the Cost Price (CP)
The shopkeeper gains 8% on the selling price.

**Formula for Cost Price:**
\[ CP = \frac{100}{100 + Gain \%} \times SP \]

**Calculating Cost Price:**
\[ CP = \frac{100}{100 + 8} \times 621 = \frac{100}{108} \times 621 \]

**Calculating:**
\[ CP = \frac{62100}{108} = 575 \]

### Step 3: Calculate Gain if No Discount is Allowed
If no discount is allowed, the selling price would be equal to the marked price.

**Selling Price without Discount:**
\[ SP_{no\ discount} = MP = 690 \]

**Calculating Gain:**
\[ Gain = SP_{no\ discount} - CP = 690 - 575 = 115 \]

### Step 4: Calculate Gain Percentage
**Formula for Gain Percentage:**
\[ Gain\% = \left( \frac{Gain}{CP} \right) \times 100 \]

**Calculating Gain Percentage:**
\[ Gain\% = \left( \frac{115}{575} \right) \times 100 \]

**Calculating:**
\[ Gain\% = \frac{11500}{575} = 20 \]

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

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