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      Question

      A trader bought an article for Rs.4000 and then marked

      it at ___% above its cost price. Thereafter he allowed two successive discounts of ___% and 25% respectively on its marked price and sold the article for Rs.1030 less than its cost price. Which of the following can fill in the blanks? I) 10 II) 12 III) 15 IV) 5
      A Only I Correct Answer Incorrect Answer
      B Only I and II Correct Answer Incorrect Answer
      C Only III Correct Answer Incorrect Answer
      D Only I and IV Correct Answer Incorrect Answer
      E All I, II, III and IV Correct Answer Incorrect Answer

      Solution

      ATQ, CP = 4000 SP = 4000 – 1030 = 2970 So, CP : SP = 4000 : 2970 = 400 : 297 If the common percentage for markup and first discount is k%, then CP/SP = (100/(100 + k)) × (100/(100 – k)) × (4/3) Now check each option: For I) k = 10 CP/SP = (100/110) × (100/90) × (4/3) = (10/11) × (10/9) × (4/3) = 400/297 (matches 400/297) For II) k = 12 CP/SP = (100/112) × (100/88) × (4/3) = (25/28) × (25/22) × (4/3) = 625/462 (≠ 400/297) For III) k = 15 CP/SP = (100/115) × (100/85) × (4/3) (not equal to 400/297) For IV) k = 5 CP/SP = (100/105) × (100/95) × (4/3) = (20/21) × (20/19) × (4/3) = 1600/1197 (≠ 400/297) So, only option I fits the blanks.

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