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. Quantity-I: The price at which 30 eggs are bought equals the price at which 18 eggs are sold. Given that a profit of Rs. 90 is made on each egg, what is the selling price for 20 eggs? Quantity-II: An individual named 'X' places an investment of Rs.2,40,000 in two separate Systematic Investment Plans (SIPs). The first SIP yields a compound interest of 20% per annum (calculated yearly), while the second provides a simple interest rate of 21% per annum. Calculate the difference in interest generated by the two SIPs after a period of 2 years.
    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 Correct Answer Incorrect Answer
    E Quantity I = Quantity II or Relation cannot be established Correct Answer Incorrect Answer

    Solution

    ATQ, Quantity I: Let the cost price of each egg be Rs. 'p' So, cost price of 30 eggs = 30 × p = Rs. '30p' Selling price of each egg = 30p ÷ 18 = Rs. '(5p/3) ' So, profit earned = (5p/3) - p = (2p/3) So, (2p/3) = 90 Or, p = 135 So, selling price of 20 eggs = (5p/3) × 20 = (5 × 135 ÷ 3) × 20 = Rs.4,500 So, Quantity I = Rs. 4,500 Quantity II: Compound interest = Sum × {1 + (rate of interest/100) } time period - Sum So, compound Interest earned = 240000 × (1.2)2 - 24000 = Rs. 1,05,600 Simple interest = Sum × rate of interest × time period in years ÷ 100 So, simple interest earned = (240000 × 21 × 2) ÷ 100 = Rs. 1,00,800 So, required difference = 105600 - 100800 = Rs. 4,800 So, Quantity II = Rs. 4,800 So, Quantity I < Quantity II

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