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 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?
Updated On: Sep 25, 2024
- 25\(\%\)
- 26.4\(\%\)
- 28.4\(\%\)
- None of these
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
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.
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.
Was this answer helpful?
0
0
Top Questions on Profit and Loss
- FS food stall sells only chicken biryani. If FS fixes a selling price of Rs. 160 per plate, 300 plates of biriyani are sold. For each increase in the selling price by Rs. 10 per plate, 10 fewer plates are sold. Similarly, for each decrease in the selling price by Rs. 10 per plate, 10 more plates are sold. FS incurs a cost of Rs. 120 per plate of biriyani, and has decided that the selling price will never be less than the cost price. Moreover, due to capacity constraints, more than 400 plates cannot be produced in a day.
If the selling price on any given day is the same for all the plates and can only be a multiple of Rs. 10, then what is the maximum profit that FS can achieve in a day? - The cost of running a movie theatre is Rs. 10,000 per day, plus additional Rs. 5000 per show. The theatre has 200 seats. A new movie released on Friday. There were three shows, where the ticket price was Rs. 250 each for the first two shows and Rs. 200 for the late-night show.
For all shows together, total occupancy was 80%. What was the maximum amount of profit possible? - Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is
- CAT - 2024
- Quantitative Aptitude
- Profit and Loss
- Bina incurs 19% loss when she sells a product at Rs. 4860 to Shyam, who in turn sells this product to Hari. If Bina would have sold this product to Shyam at the purchase price of Hari, she would have obtained 17% profit. Then, the profit, in rupees, made by Shyam is
- CAT - 2024
- Quantitative Aptitude
- Profit and Loss
- The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is
- CAT - 2024
- Quantitative Aptitude
- Profit and Loss
View More Questions
Questions Asked in MAT exam
- In the following sentence, a part of the sentence is underlined. Beneath each sentence four different ways of phrasing the underlined part are indicated. Choose the best alternative among the four options.
There \(\underline {\text{have}\ \text{been}\ \text{heavy}\ \text{rainfall}}\) yesterday- MAT - 2018
- Sentence Correction
- Who among the following cannot be impeached?
- MAT - 2018
- Politics and Government
- Who is leading the LTTE delegation for the peace process with Sri Lanka?
- MAT - 2018
- International Organizations
- Who was the first UN Secretary General?
- MAT - 2018
- Politics and Government
- Which of the following sources yields the maximum revenue to the Union Government?
- MAT - 2018
- Politics and Government
View More Questions