The price of a bicycle was $456. The trader first decreased the price

Price of bicycle = 456
25% decrease = 456-114 = 342
25% increase = 342+85.5 = 427.5

Initial Price = 456
Final Price = 427.5
% Change = (456-427.5)/456 = 6.25% change

Answer : A

The price of bicycle is irrelevant and extraneous. It is purely a percentage question.

Solution:

The price of the bicycle is a red herring; it can be any number. If we let it be x, then the final price of the bicycle is x * 0.75 * 1.25 = x * 0.9375 = 0.9735x. We can see that the final price of 0.9375x is 93.75% of the initial price of x. Thus, the final percent change in the price of the bicycle is 1 - 0.9375 = 0.0625, or 6.25%.

Alternate Solution:

Let’s assume the original cost of the bike is $160. After a 25% price drop, the bike is selling for 160 x 3/4 = $120. Now, if that reduced price is increased by 25%, the revised, final price of the bike is 120 x 5/4 = $150.

We can use the percent change formula: (New - Old)/Old x 100% to determine the final percent change in the price of the bicycle:

(150 - 160)/150 x 100% = -10/160 x 100% = -6.25%, which is a 6.25% decrease.

Answer: A

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