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3 Must Learn Applications of Percentages - Exercise Question #1

1- Alex bought a smartwatch at $200 from his friend and sold it to another friend at a certain price. What is his actual profit percentage?
    1. Alex gave a discount of 25% while selling the watch.
    2. Alex made a profit of 33.3%, when calculated on the selling price.

Options

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.


Read More about Percentages and its application


Article-1: 3 Major Concerns Students Face in Solving Percentage Problems

So CP for Alex = 200, SP not given.

(1) Gave a discount of 1/4 on Marked Price to sell, but since we dont know the Marked price, we cannot calculate SP. Not sufficient.

(2) Suppose SP=x. Profit is = x/3. This means CP + x/3 = x
or 200 + x/3 = x. Or x=300. So profit = 100 on CP of 200, and thus actual profit percentage = 50%. Sufficient.

Hence B answer
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Statement 1: What's the discount on? a sale price of $1,000? $10,000?
Statement 2: Profit is 33.3% (1/3) so it's 4/3 of the purchase price. Profit = 4/3(200) = $266.67 which is 66/200 or 33% greater than 200.

B
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Strangely phrased question. Too wordy IMO.

"Alex made a profit of 33.3%, when calculated on the selling price." - How does this make sense ? One is supposed to infer : Alex made a profit which is equal to 33.33 % of the selling price.
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S2 is weird. While I understand what S2 is trying to test. IMO profit is calculated on Cost price and not on Selling price.
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