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The single discount equal to three consecutive discounts of 10%, 12% and 5% is
- a)16.274%
- b)24.76%
- c)4.76%
- d)12%
Correct answer is option 'B'. Can you explain this answer?
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Understanding Consecutive Discounts
When applying multiple discounts consecutively, the total discount is not simply the sum of the percentages. Instead, each discount is applied to the remaining amount after the previous discount.
Calculating the Effective Single Discount
Let's break down the discounts step by step:
1. Initial Price: Assume the original price is 100 (for simplicity).
2. First Discount - 10%:
- Discounted Amount: 10% of 100 = 10
- Price After Discount: 100 - 10 = 90
3. Second Discount - 12%:
- Discounted Amount: 12% of 90 = 10.8
- Price After Discount: 90 - 10.8 = 79.2
4. Third Discount - 5%:
- Discounted Amount: 5% of 79.2 = 3.96
- Price After Discount: 79.2 - 3.96 = 75.24
Calculating the Overall Discount
Now, to find the total discount from the original price:
- Total Discount: 100 - 75.24 = 24.76
Calculating the Single Equivalent Discount Percentage
To find the single discount percentage:
- Single Discount Percentage: (Total Discount / Original Price) * 100
- Calculation: (24.76 / 100) * 100 = 24.76%
Thus, the single discount equivalent to the three consecutive discounts of 10%, 12%, and 5% is 24.76%.
This means option 'b' is the correct answer.
When applying multiple discounts consecutively, the total discount is not simply the sum of the percentages. Instead, each discount is applied to the remaining amount after the previous discount.
Calculating the Effective Single Discount
Let's break down the discounts step by step:
1. Initial Price: Assume the original price is 100 (for simplicity).
2. First Discount - 10%:
- Discounted Amount: 10% of 100 = 10
- Price After Discount: 100 - 10 = 90
3. Second Discount - 12%:
- Discounted Amount: 12% of 90 = 10.8
- Price After Discount: 90 - 10.8 = 79.2
4. Third Discount - 5%:
- Discounted Amount: 5% of 79.2 = 3.96
- Price After Discount: 79.2 - 3.96 = 75.24
Calculating the Overall Discount
Now, to find the total discount from the original price:
- Total Discount: 100 - 75.24 = 24.76
Calculating the Single Equivalent Discount Percentage
To find the single discount percentage:
- Single Discount Percentage: (Total Discount / Original Price) * 100
- Calculation: (24.76 / 100) * 100 = 24.76%
Thus, the single discount equivalent to the three consecutive discounts of 10%, 12%, and 5% is 24.76%.
This means option 'b' is the correct answer.
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The single discount equal to three consecutive discounts of 10%, 12% and 5% isa)16.274%b)24.76%c)4.76%d)12%Correct answer is option 'B'. Can you explain this answer?
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