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vitorcbarbieri
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21 Nov 2017, 15:05
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How to solve the question below using sucessive discounts formula?
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
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
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21 Nov 2017, 15:58
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vitorcbarbieri
vitorcbarbieri - The question is a little confusing. There are two sell prices: one before the discount ("marked price") the other, after the discount.
The "marked price" gives you the cost of the item. Discounted price gives you the profit. And you derive the marked price from the discount price.
Actual discounted price yields original price
Marked price before successive discounts of 20 and 30 percent?
(I think the following formula is what you're after. Not positive.)*
(a + b + \(\frac{ab}{100})\) percent
\((20 + 30 + \frac{600}{100})\) percent
\((20 + 30 + 6) = 56\) percent
The discounted price is 56% of original marked price, call it x
$112 = .56x
\(\frac{$112}{(\frac{56}{100})}= 112 *\frac{100}{56}=$200\) = original price
Cost price?
The marked price is 100% higher than the cost price, c.
$200 = c + \(\frac{100}{100}\)c = 2c
$200 = 2c
c = $100
Profit?
Sell Price - Cost Price
$112 - 100 = $12
Answer A
Hope it helps.
*You can also derive this discount percentage by taking: 1) first discount: 1 - .20 = .80; 2) second discount: 1 - .30 = .70. Multiply them: (.8 * .7) = .56
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