A fan is listed at Rs. 1400 and the discount offered is `10%` What additional discount must be given to bring the net selling price to Rs. 1200 ?

Options

A. `16(2)/(3)%`
B. `5%`
C. `4(16)/(21)%`
D. `6%`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the initial selling price after the first discount.
The listed price of the fan is Rs. 1400, and the discount offered is 10%.

**Calculation:**
- Discount = 10% of Rs. 1400
- Discount = (10/100) * 1400 = Rs. 140

Now, we subtract the discount from the listed price to find the selling price after the discount.

- Selling Price after discount = Listed Price - Discount
- Selling Price after discount = 1400 - 140 = Rs. 1260

### Step 2: Determine the required selling price.
We want the net selling price to be Rs. 1200.

### Step 3: Calculate the difference between the selling price after the first discount and the required selling price.
**Calculation:**
- Difference = Selling Price after discount - Required Selling Price
- Difference = 1260 - 1200 = Rs. 60

### Step 4: Calculate the additional discount percentage needed to achieve the required selling price.
Let the additional discount be X%.

We know that the additional discount of X% on the selling price after the first discount (which is Rs. 1260) should equal Rs. 60.

**Calculation:**
- Additional Discount = X% of Rs. 1260
- (X/100) * 1260 = 60

Now, we can solve for X:
- X * 1260 = 60 * 100
- X * 1260 = 6000
- X = 6000 / 1260
- X = 4.76 (approximately)

### Step 5: Convert the decimal to a fraction.
To express 4.76% as a fraction:
- 4.76% = 4 + (76/100)%
- 4.76% = 4 + (19/25)%
- Convert to a common denominator if necessary.

### Conclusion:
The additional discount required to bring the net selling price to Rs. 1200 is approximately 4.76%, which can be expressed as \(4 \frac{16}{21}\%\).