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The marked price of a garment is 100% higher than the cost price. If it is sold at a price of $112 after applying successive discounts of 20% and 30% on the marked price, what is the profit (in dollars) obtained by selling the garment?
- a)12
- b)32
- c)54
- d)88
- e)100
Correct answer is option 'A'. Can you explain this answer?
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The marked price of a garment is 100% higher than the cost price. If i...
Given:
- Marked price of the garment is 100% higher than the cost price.
- The garment is sold at a price of $112 after applying successive discounts of 20% and 30% on the marked price.
To find:
The profit obtained by selling the garment.
Solution:
1. Let's assume the cost price of the garment is $x.
2. The marked price of the garment is 100% higher than the cost price, so the marked price will be $x + 100% of x, which is $x + x = $2x.
3. The first discount of 20% is applied on the marked price, so the selling price after the first discount will be 80% of the marked price.
- Selling price after the first discount = 80% of $2x = 0.8 * $2x = $1.6x.
4. The second discount of 30% is applied on the selling price after the first discount, so the final selling price will be 70% of the selling price after the first discount.
- Final selling price = 70% of $1.6x = 0.7 * $1.6x = $1.12x.
5. Given that the final selling price is $112, we can equate it to $1.12x and solve for x:
- $1.12x = $112
- x = $112 / $1.12
- x = $100
6. The cost price of the garment is $100.
7. Profit = Selling price - Cost price
- Profit = $112 - $100
- Profit = $12
Answer:
The profit obtained by selling the garment is $12. Therefore, the correct answer is option A.
- Marked price of the garment is 100% higher than the cost price.
- The garment is sold at a price of $112 after applying successive discounts of 20% and 30% on the marked price.
To find:
The profit obtained by selling the garment.
Solution:
1. Let's assume the cost price of the garment is $x.
2. The marked price of the garment is 100% higher than the cost price, so the marked price will be $x + 100% of x, which is $x + x = $2x.
3. The first discount of 20% is applied on the marked price, so the selling price after the first discount will be 80% of the marked price.
- Selling price after the first discount = 80% of $2x = 0.8 * $2x = $1.6x.
4. The second discount of 30% is applied on the selling price after the first discount, so the final selling price will be 70% of the selling price after the first discount.
- Final selling price = 70% of $1.6x = 0.7 * $1.6x = $1.12x.
5. Given that the final selling price is $112, we can equate it to $1.12x and solve for x:
- $1.12x = $112
- x = $112 / $1.12
- x = $100
6. The cost price of the garment is $100.
7. Profit = Selling price - Cost price
- Profit = $112 - $100
- Profit = $12
Answer:
The profit obtained by selling the garment is $12. Therefore, the correct answer is option A.
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The marked price of a garment is 100% higher than the cost price. If it is sold at a price of $112 after applying successive discounts of 20% and 30% on the marked price, what is the profit (in dollars) obtained by selling the garment?a)12b)32c)54d)88e)100Correct answer is option 'A'. Can you explain this answer?
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