Question

A shopkeeper sold a TV set for Rs. 17,940, with a discount of 8$\%$ and gained 19.6$\%$. If no discount is allowed, then what will be his gain per cent?

• A. 25$\%$
• B. 26.4$\%$
• C. 28.4$\%$
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

The correct option is (D): None of these
Explanation:To find the shopkeeper's gain percentage without the discount, we can follow these steps:
1. Calculate the marked price (MP):
The selling price (SP) is given as Rs. 17,940 after an 8% discount.
Using the formula for selling price after discount:
$SP = MP \times \left(1 - \frac{d}{100}\right)$
where $d$ is the discount percentage.
Rearranging the formula gives:
$MP = \frac{SP}{1 - \frac{d}{100}} = \frac{17940}{1 - 0.08} = \frac{17940}{0.92} = 19500$
2. Calculate the cost price (CP):
Given that the gain is 19.6%, we can find the cost price using the relationship:
$SP = CP \times \left(1 + \frac{g}{100}\right)$
where $g$ is the gain percentage.
Rearranging the formula gives:
$CP = \frac{SP}{1 + \frac{g}{100}} = \frac{17940}{1 + 0.196} = \frac{17940}{1.196} \approx 14980$
3. Calculate the gain when no discount is allowed:
If no discount is allowed, the selling price is equal to the marked price (Rs. 19,500). The gain in this case would be:
$\text{Gain} = MP - CP = 19500 - 14980 = 4500$
4. Calculate the gain percentage:
Now, we can find the gain percentage using the formula:
$\text{Gain percentage} = \left(\frac{\text{Gain}}{CP}\right) \times 100 = \left(\frac{4500}{14980}\right) \times 100 \approx 30.05\%$
Therefore, the Correct answer is Option D: None of these.