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

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Math Expert
Joined: 02 Sep 2009
Posts: 58428
The original cost of a coat was increased by 40% at the beginning of 2  [#permalink]

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25 Nov 2018, 21:34
00:00

Difficulty:

55% (hard)

Question Stats:

64% (02:38) correct 36% (03:19) wrong based on 77 sessions

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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]

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25 Nov 2018, 21:44
1
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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Joined: 30 Jul 2017
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Location: India
Re: The original cost of a coat was increased by 40% at the beginning of 2  [#permalink]

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27 Nov 2018, 06:20
x*(140/100)*(80/100) = (50+95.60)
x = 130
Intern
Joined: 20 Jun 2017
Posts: 2
Re: The original cost of a coat was increased by 40% at the beginning of 2  [#permalink]

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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
Intern
Joined: 03 Sep 2018
Posts: 7
Re: The original cost of a coat was increased by 40% at the beginning of 2  [#permalink]

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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

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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