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A dealer offers a discount of 20%, 10% and 5%. What is the single equivalent rate of discount?
- a)32.6%
- b)31.6%
- c)28.6%
- d)33.6%
Correct answer is option 'B'. Can you explain this answer?
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Understanding Discounts
When multiple discounts are applied sequentially, the overall effect is not simply the sum of the discounts. Instead, we need to calculate the final price after each discount to find the equivalent single discount rate.
Calculating the Final Price
1. Original Price (P): Assume the original price is 100 (for ease of calculation).
2. First Discount (20%):
- Price after first discount = P - (20% of P)
- Price = 100 - (20/100 * 100) = 100 - 20 = 80
3. Second Discount (10%):
- Price after second discount = Current Price - (10% of Current Price)
- Price = 80 - (10/100 * 80) = 80 - 8 = 72
4. Third Discount (5%):
- Price after third discount = Current Price - (5% of Current Price)
- Price = 72 - (5/100 * 72) = 72 - 3.6 = 68.4
Final Price Calculation
- After applying all discounts, the final price is 68.4.
Calculating the Total Discount
- Total Discount = Original Price - Final Price
- Total Discount = 100 - 68.4 = 31.6
Equivalent Single Discount Rate
- To find the equivalent single discount rate, use the formula:
- Equivalent Discount Rate = (Total Discount / Original Price) * 100
- Equivalent Discount Rate = (31.6 / 100) * 100 = 31.6%
Conclusion
The single equivalent discount rate when applying 20%, 10%, and 5% sequentially is 31.6%, confirming option 'B' as the correct answer.
When multiple discounts are applied sequentially, the overall effect is not simply the sum of the discounts. Instead, we need to calculate the final price after each discount to find the equivalent single discount rate.
Calculating the Final Price
1. Original Price (P): Assume the original price is 100 (for ease of calculation).
2. First Discount (20%):
- Price after first discount = P - (20% of P)
- Price = 100 - (20/100 * 100) = 100 - 20 = 80
3. Second Discount (10%):
- Price after second discount = Current Price - (10% of Current Price)
- Price = 80 - (10/100 * 80) = 80 - 8 = 72
4. Third Discount (5%):
- Price after third discount = Current Price - (5% of Current Price)
- Price = 72 - (5/100 * 72) = 72 - 3.6 = 68.4
Final Price Calculation
- After applying all discounts, the final price is 68.4.
Calculating the Total Discount
- Total Discount = Original Price - Final Price
- Total Discount = 100 - 68.4 = 31.6
Equivalent Single Discount Rate
- To find the equivalent single discount rate, use the formula:
- Equivalent Discount Rate = (Total Discount / Original Price) * 100
- Equivalent Discount Rate = (31.6 / 100) * 100 = 31.6%
Conclusion
The single equivalent discount rate when applying 20%, 10%, and 5% sequentially is 31.6%, confirming option 'B' as the correct answer.
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A dealer offers a discount of 20%, 10% and 5%. What is the single equivalent rate of discount?a)32.6%b)31.6%c)28.6%d)33.6%Correct answer is option 'B'. Can you explain this answer?
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