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      Question

      In the question, two Quantities I and II are given. You

      have to solve both the Quantity to establish the correct relation between Quantity-I and Quantity-II and choose the correct option. On a certain article, the percentage of profit earned on selling it is 'a'% and the percentage of discount offered on its marked price is 'b'%. We have, a:b = 8:5 and the marked price of the item is 65% more than its cost price and the selling price of the article is Rs. 2816 more than its cost price. Quantity I: If the seller marks the price of the item by 50% more than its cost price and allows the discount of 30%, then find the new selling price of the item. Quantity II: If the value of 'z' is Rs. 104 less than the original amount of discount given, then find the value of 3z.
      A Quantity-I > Quantity-II Correct Answer Incorrect Answer
      B Quantity-I < Quantity-II Correct Answer Incorrect Answer
      C Quantity-I ≤ Quantity-II Correct Answer Incorrect Answer
      D Quantity-I = Quantity-II or No relation Correct Answer Incorrect Answer
      E Quantity-I ≥ Quantity-II Correct Answer Incorrect Answer

      Solution

      Let, the cost price, Selling Price, and Marked price of the item be CP, SP, and MP respectively. MP = (165/100) X CP Let, a = 8y and let b = 5y respectively. ATQ, (165/100) = (100 + 8y) /(100 - 5y) (33/20) = (100 + 8y) /(100 - 5y) 3300 - 165y = 2000 + 160y 325y = 1300 y = 4 Discount percentage = 5y = 20 Profit percentage = 8y = 32 So, CP = 2816 X (100/32) = Rs. 8800 SP = 8800 + 2816 = Rs. 11616 MP = (165/100) X 8800 = Rs. 14520 Quantity I: CP = Rs. 8800 If the marked price of the item is 50% more than the cost price of the item, Marked Price = 1.50 X 8800 = Rs. 13200 Now, the Discount Percentage = 30% So, Selling Price = 0.70 X 13200 = Rs. 9240 So, Quantity I = Rs. 9240 Quantity II: Original discount amount = 14520 - 11616 = Rs. 2904 So, z = (2904 - 104) z = 2800 3z = 3 X 2800 = Rs. 8400 So, Quantity II = Rs. 8400 Hence, Quantity-I > Quantity-II

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