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A discount series of 15%, 20% and 30% is equal to a single discount of:
- a)50%
- b)47.6%
- c)52.8%
- d)52.4%
Correct answer is option 'D'. Can you explain this answer?
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A discount series of 15%, 20% and 30% is equal to a single discount of...
**Solution:**
Let's assume the original price of an item is $100.
**First discount of 15%:**
The price after the first discount of 15% would be: $100 - (15/100) * $100 = $100 - $15 = $85.
**Second discount of 20%:**
The price after the second discount of 20% would be: $85 - (20/100) * $85 = $85 - $17 = $68.
**Third discount of 30%:**
The price after the third discount of 30% would be: $68 - (30/100) * $68 = $68 - $20.4 = $47.6.
So, the final price after all three discounts is $47.6.
Now, let's calculate the single discount that would give the same final price.
Let's assume this single discount is x%.
The price after a single discount of x% would be: $100 - (x/100) * $100.
We need to find the value of x that makes the final price $47.6.
$100 - (x/100) * $100 = $47.6
Divide both sides of the equation by $100:
1 - x/100 = 0.476
Subtract 1 from both sides:
-x/100 = -0.524
Multiply both sides by 100:
-x = -52.4
Divide both sides by -1:
x = 52.4
Therefore, a single discount of 52.4% is equivalent to the series of discounts of 15%, 20%, and 30%.
Hence, the correct option is D) 52.4%.
Let's assume the original price of an item is $100.
**First discount of 15%:**
The price after the first discount of 15% would be: $100 - (15/100) * $100 = $100 - $15 = $85.
**Second discount of 20%:**
The price after the second discount of 20% would be: $85 - (20/100) * $85 = $85 - $17 = $68.
**Third discount of 30%:**
The price after the third discount of 30% would be: $68 - (30/100) * $68 = $68 - $20.4 = $47.6.
So, the final price after all three discounts is $47.6.
Now, let's calculate the single discount that would give the same final price.
Let's assume this single discount is x%.
The price after a single discount of x% would be: $100 - (x/100) * $100.
We need to find the value of x that makes the final price $47.6.
$100 - (x/100) * $100 = $47.6
Divide both sides of the equation by $100:
1 - x/100 = 0.476
Subtract 1 from both sides:
-x/100 = -0.524
Multiply both sides by 100:
-x = -52.4
Divide both sides by -1:
x = 52.4
Therefore, a single discount of 52.4% is equivalent to the series of discounts of 15%, 20%, and 30%.
Hence, the correct option is D) 52.4%.
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A discount series of 15%, 20% and 30% is equal to a single discount of:a)50%b)47.6%c)52.8%d)52.4%Correct answer is option 'D'. Can you explain this answer?
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