nick1816 wrote:
A shopkeeper bought an article for Rs.1000 and marked its price as Rs.2160. He gave three successive discounts of a%, b% and c%, where a + b + c = 50. If he made a profit of x% finally, then what is the difference between maximum value of x and minimum value of x ?
A. 10
B. 17
C. 24
D. 30
E. 33.33
Recall that the order in which we apply the discount doesn’t matter (for example, a discount of 10% followed by a discount of 20% is same as a discount of 20% followed by a discount of 10%). Also, let’s assume that any values of a, b, and c can be 0 and they can also be decimals or fractions.
The minimum discounted price of the article after 3 discounts occurs when a, b, and c are as far apart as possible. That is, if we let a = 50, b = 0, and c = 0, then the minimum discounted price is 2160 x 0.5 x 1 x 1 = 1080.
The maximum discounted price of the article after 3 discounts occurs when a, b, and c are as close to each other as possible. That is, if we let a = b = c = 50/3 = 16⅔ (notice that 16⅔% = 1/6), then the maximum discounted price is 2160 x 5/6 x 5/6 x 5/6 = 2160 x 125/216 = 1250.
In the first case (minimum discounted price), the profit is 80, so the profit margin is 8%. In other words, the minimum value of x is 8. In the latter case (maximum discounted price), the profit is 250, so the profit margin is 25%. In other words, the maximum value of x is 25.
So the difference between the maximum and minimum values of x is 25 - 8 = 17.
Answer: B _________________
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