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The ratio of cost price and marked price of a cell phone is 2 : 3 and ratio of profit percentage and discount percentage is 3 : 2. What is the discount percentage?
- a)8%
- b)12%
- c)16.66%
- d)19.5%
Correct answer is option 'C'. Can you explain this answer?
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The ratio of cost price and marked price of a cell phone is 2 : 3 and...
Given:
- The ratio of cost price and marked price of a cell phone is 2:3.
- The ratio of profit percentage and discount percentage is 3:2.
To find:
The discount percentage.
Solution:
Let's assume the cost price of the cell phone is 2x and the marked price is 3x.
Selling Price:
The selling price is the marked price minus the discount.
Let's assume the discount percentage is d%.
So, the selling price will be (100 - d)% of the marked price.
Therefore, the selling price is (100 - d)% of 3x, which is (100 - d) * 3x / 100.
Profit:
Profit is the selling price minus the cost price.
Profit = Selling Price - Cost Price
Profit = (100 - d) * 3x / 100 - 2x
Profit = (300 - 3d)x/100 - 2x
Profit = (300 - 3d - 200)x/100
Profit = (100 - 3d)x/100
Profit Percentage:
Profit percentage is the profit divided by the cost price multiplied by 100.
Profit Percentage = (Profit / Cost Price) * 100
Profit Percentage = [(100 - 3d)x/100 / 2x] * 100
Profit Percentage = (100 - 3d)/2
Given, Profit Percentage : Discount Percentage = 3:2
(100 - 3d)/2 = 3/2
100 - 3d = 3
-3d = 3 - 100
-3d = -97
d = -97/-3
d = 32.33
The discount percentage is 32.33%, which is approximately 16.66%.
Therefore, the correct answer is option (C) 16.66%.
- The ratio of cost price and marked price of a cell phone is 2:3.
- The ratio of profit percentage and discount percentage is 3:2.
To find:
The discount percentage.
Solution:
Let's assume the cost price of the cell phone is 2x and the marked price is 3x.
Selling Price:
The selling price is the marked price minus the discount.
Let's assume the discount percentage is d%.
So, the selling price will be (100 - d)% of the marked price.
Therefore, the selling price is (100 - d)% of 3x, which is (100 - d) * 3x / 100.
Profit:
Profit is the selling price minus the cost price.
Profit = Selling Price - Cost Price
Profit = (100 - d) * 3x / 100 - 2x
Profit = (300 - 3d)x/100 - 2x
Profit = (300 - 3d - 200)x/100
Profit = (100 - 3d)x/100
Profit Percentage:
Profit percentage is the profit divided by the cost price multiplied by 100.
Profit Percentage = (Profit / Cost Price) * 100
Profit Percentage = [(100 - 3d)x/100 / 2x] * 100
Profit Percentage = (100 - 3d)/2
Given, Profit Percentage : Discount Percentage = 3:2
(100 - 3d)/2 = 3/2
100 - 3d = 3
-3d = 3 - 100
-3d = -97
d = -97/-3
d = 32.33
The discount percentage is 32.33%, which is approximately 16.66%.
Therefore, the correct answer is option (C) 16.66%.
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The ratio of cost price and marked price of a cell phone is 2 : 3 and ratio of profit percentage and discount percentage is 3 : 2. What is the discount percentage?a)8%b)12%c)16.66%d)19.5%Correct answer is option 'C'. Can you explain this answer?
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