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# M19-10

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Math Expert
Joined: 02 Sep 2009
Posts: 54369

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16 Sep 2014, 01:05
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15% (low)

Question Stats:

81% (01:24) correct 19% (01:25) wrong based on 185 sessions

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If the price of a car includes a 20% mark-up, by what percent will the price of the car be reduced if the mark-up is cut in half?

A. $$5$$
B. $$8 \frac{1}{3}$$
C. $$12$$
D. $$14 \frac{1}{3}$$
E. $$15 \frac{2}{3}$$

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Math Expert
Joined: 02 Sep 2009
Posts: 54369

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16 Sep 2014, 01:05
Official Solution:

If the price of a car includes a 20% mark-up, by what percent will the price of the car be reduced if the mark-up is cut in half?

A. $$5$$
B. $$8 \frac{1}{3}$$
C. $$12$$
D. $$14 \frac{1}{3}$$
E. $$15 \frac{2}{3}$$

If $$x$$ is the price of the car without the mark-up, then its price with the mark-up is $$1.2x$$. If the mark-up is cut in half, the price of the car will drop to $$1.1x$$ and be reduced by $$\frac{1.2x - 1.1x}{1.2x} = \frac{1}{12}$$ or $$\frac{100}{12}\% = 8 \frac{1}{3}\%$$.

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Joined: 02 Sep 2016
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04 Oct 2016, 17:43
how will the markup be 1.1x after reducing to half?
Intern
Joined: 24 Oct 2016
Posts: 1

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29 Oct 2016, 10:47
3
manchitkapoor wrote:
how will the markup be 1.1x after reducing to half?

I like to use numbers in cases like this. I chose 100 as the original car price since it makes things easy. A 20% markup would make the car $120. If the mark-up is reduced by half (20% to 10%), the car is now priced at$110. So percent change is clearly less than 10% but greater than 5% so you don't really need to do much more math then that.
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Joined: 04 Dec 2015
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Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
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04 Aug 2017, 06:25
Bunuel wrote:
If the price of a car includes a 20% mark-up, by what percent will the price of the car be reduced if the mark-up is cut in half?

A. $$5$$
B. $$8 \frac{1}{3}$$
C. $$12$$
D. $$14 \frac{1}{3}$$
E. $$15 \frac{2}{3}$$

Let the initial price of car be $$= 100$$

Price of car after $$20$$% mark-up $$= 120$$% of $$100 = \frac{120}{100} * 100 = 120$$

If the mark-up is cut in half, ie; $$10$$%, price of car $$= 110$$% of $$100 = \frac{110}{100} * 100 = 110$$

Required percentage $$=$$ ( Difference of price after mark-up cut $$/$$ Price of car after $$20$$% mark-up ) $$* 100$$

Required percentage $$= \frac{120 - 110}{120} * 100 = \frac{10}{120} * 100 = \frac{25}{3}$$ or $$8 \frac{1}{3}$$

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04 Aug 2017, 06:42
Assume the price to be x. Mark up becomes 0.2x. If the mark up is half , the amount becomes 1.1x. The reduction percentage is then (0.1x/1.2x)*100. So it becomes 100/12 or option B.
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Re: M19-10   [#permalink] 04 Aug 2017, 06:42
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# M19-10

Moderators: chetan2u, Bunuel

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