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# M19-10

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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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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 $$8 \frac{1}{3}$$