Multiple choice

The ratio of the marked price to the cost price of a book is 7 : 5. When it is sold at % discount, then x% profit is obtained and when it is sold at _% discount, then (x - 7)% profit is obtained. Which of the following options are possible for the blanks in the same order? A. 15, 20 B. 16, 21 C. 20, 25 D. 10, 20

  1. A and B

  2. A, B and D

  3. A, B and C

  4. Only B

  5. Only C
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let CP = 5k and MP = 7k. Profit = SP - CP. For option A (15% discount), SP = 0.85 * 7k = 5.95k, Profit = 0.95k (19%). For B (16% discount), SP = 0.84 * 7k = 5.88k, Profit = 0.88k (17.6%). For C (20% discount), SP = 0.8 * 7k = 5.6k, Profit = 0.6k (12%). Testing the pairs shows A, B, and C satisfy the conditions for x and x-7.

AI explanation

Assume the cost price is 500 and the marked price is 700. We check option C (20 percent discount) by calculating the selling price as 700 times 0.80, which is 560 for a 12 percent profit. We then check option B (16 percent discount) by calculating the selling price as 700 times 0.84, which is 588 for a 17.6 percent profit. We also check option A (15 percent discount) by calculating the selling price as 700 times 0.85, which is 595 for a 19 percent profit. Finally, checking option D (10 percent discount) gives a selling price of 630 for a 26 percent profit. Since the profits for the first three options differ by 7 percent, 5.6 percent, and 5 percent respectively, options A, B, and C are all valid possible values for the given conditions.

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