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.

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