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    Question

    Pawan, Qureshi, and Ram

    started a business with initial investments of Rs. (x + 1500), Rs. x, and Rs. (x - 1000), respectively. Quantity I: Given that the total profit after one year is Rs. 17,760, and Qureshi's share of the profit is Rs. 5,760, determine Pawan's initial investment. Quantity II: If Pawan, Qureshi, and Ram invested their amounts for y, 2y, and 3y months, respectively, and Ram's profit share is Rs. 10,000 from a total profit of Rs. 23,750, find the initial investment made by Qureshi. In the question, two quantities i.e. Quantity I and Quantity II are given. Solve the given quantities to establish the correct relation between them and choose the correct option.
    A Quantity I > Quantity II Correct Answer Incorrect Answer
    B Quantity I < Quantity II Correct Answer Incorrect Answer
    C Quantity I = Quantity II or No relation can be established Correct Answer Incorrect Answer
    D Quantity I ≥ Quantity II Correct Answer Incorrect Answer
    E Quantity I ≤ Quantity II Correct Answer Incorrect Answer

    Solution

    ATQ, Quantity I, x/(3x + 500) = 5760/17760 = 12/37 37x = 36x + 6000 x = 6000 Initial Investment of Pawan = 6000 + 1500 = Rs.7500 Quantity II, {(x - 1000) × 3y}/{(x + 1500) × y + x × 2y + (x - 1000) × 3y} = 10000/23750 3(x - 1000)/(x + 1500 + 2x + 3x - 3000) = 8/19 3(x - 1000)/(6x - 1500) = 8/19 19 × (x - 1000) = 8 × (2x - 500) 19x - 19000 = 16x - 4000 3x = 15000 x = 5000 Amount Invested by Qureshi = x = Rs.5000 Quantity I > Quantity II

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