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The original cost of a coat was increased by 40% at the beginning of 2

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Bunuel
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The original cost of a coat was increased by 40% at the beginning of 2 [#permalink] New post   25 Nov 2018, 21:34
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The original cost of a coat was increased by 40% at the beginning of 2015. In March 2015, the new price was reduced by 20%, and the cost remained at this new reduced price. Chris had a coupon for a $ 50 discount and, in April, used the coupon to buy the coat at the further reduced price. There was no tax or additional fee on the purchase. If Chris paid $ 95.60 for the coat, which would be the original price of the coat?

A. $ 2.50

B. $100

C. $104.83

D. $120

E. $130
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Re: The original cost of a coat was increased by 40% at the beginning of 2 [#permalink] New post   25 Nov 2018, 21:44
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Let the original price of the coat before 2015 be "x".
At the beginning of 2015, the price went to "1.4x"

Now the price reduced by 20%. So 0.8*1.4x = 1.12x

Chris has $50 coupon. He paid $95.6.

1.12x - $50 = $95.6
1.12x = 145.6
x = $130

OPTION: E
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Re: The original cost of a coat was increased by 40% at the beginning of 2 [#permalink] New post   17 Feb 2021, 17:23
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Bunuel wrote:
The original cost of a coat was increased by 40% at the beginning of 2015. In March 2015, the new price was reduced by 20%, and the cost remained at this new reduced price. Chris had a coupon for a $ 50 discount and, in April, used the coupon to buy the coat at the further reduced price. There was no tax or additional fee on the purchase. If Chris paid $ 95.60 for the coat, which would be the original price of the coat?

A. $ 2.50

B. $100

C. $104.83

D. $120

E. $130


Solution:


Since Chris paid $95.60 for the coat after the $50 coupon, the price of the coat before the coupon would be 95.6 + 50 = $145.60. Since this price is after a reduction of 20% from the previous price, the previous price is 145.6/0.8 = $182. Finally, since $182 is after an increase of 40% from the original price, the original price of the coat is 182/1.4 = $130.

Answer: E
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Re: The original cost of a coat was increased by 40% at the beginning of 2 [#permalink] New post   27 Nov 2018, 06:20
x*(140/100)*(80/100) = (50+95.60)
x = 130
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Re: The original cost of a coat was increased by 40% at the beginning of 2 [#permalink] New post   27 Nov 2018, 18:43
Original Price = X
Increase by 40% = 1.4X and then
Decreased by 20% = 0.8(1.40) = 1.12X
1.12X -50 = 95.60
1.12X = 95.60 + 50
x ~ 146/1.12 = 130
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Re: The original cost of a coat was increased by 40% at the beginning of 2 [#permalink] New post   15 Jan 2019, 17:35
This is how I answered this in 30 seconds.

Sale Price: 50 + 95 = 145 (who really cares about the decimal?)

Looking at the way the original price was increased and decreased answer E looked like a good candidate to try...

Original Price: 130 (note: 10% of 130 = 13)
40% of 130 = 4 * 10% = 4 * 13 = 52
Increased Price: 130 + 52 = 182 (note: 10% of 182 = 18)
20% of 182 = 2 * 18 = 36
Decreased Price (Sale Price): 182 - 36 = 146

146... looks good! Answer E.
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Re: The original cost of a coat was increased by 40% at the beginning of 2 [#permalink]
15 Jan 2019, 17:35
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