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      Question

      Ratio of cost price of two items P and Q is 2:5. Item P

      and Item Q are marked 25% above and 30% above their respective cost price. If the ratio of discount percent allowed on item P to item Q is 1:2 and profit made on the items P & Q is 12.5% & 4% respectively, then find which of the following statement/s is /are true. (Note: discount percentage on item P is ‘d’ %) (i) Value of ‘d’ is odd number. (ii) Value of ‘d’ is prime number. (iii) ‘d’ is less than 12 and greater than 8
      A Only II Correct Answer Incorrect Answer
      B Only III Correct Answer Incorrect Answer
      C Both I and III Correct Answer Incorrect Answer
      D Both I and II Correct Answer Incorrect Answer
      E All of these above Correct Answer Incorrect Answer

      Solution

      Let cost price of P & Q be 200x and 500x respectively  Marked price of P =  200x × (125/100) = 250x Marked price of Q = 500x×130/100=650x ATQ, [250x×((100-d))/100+650x×((100-2d))/100]=200x×112.5/100+500x×104/100 [2.5x×(100-d)+6.5x×(100-2d) ]=225x+520x [250x-2.5xd+650x-13xd]=745x   155x=15.5xd  10=d   From (i) d = 10 10 is not an odd number. From (ii) d = 10 10 is not a prime number.  From (ii) d = 10 ‘d’ is less than 12 and greater than 8. So, only (iii)

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