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      Question

      Arjun, Bheem, and Chetan start a business with initial

      investments of Rs. (p+1500), Rs. 'p', and Rs. (p-1000) respectively. Quantity I: If the total profit after one year is Rs. 17,760, and Bheem's profit share is Rs. 5,760, what was Arjun's initial investment? Quantity II: If Arjun, Bheem, and Chetan invested their amounts for 'm' months, '2m' months, and '3m' months respectively, and Chetan's profit share is Rs. 10,000 from a total profit of Rs. 23,750, what was Bheem's initial investment? 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 Correct Answer Incorrect Answer
      D Quantity I ≥ Quantity II Correct Answer Incorrect Answer
      E Quantity I = Quantity II or relation cant be established Correct Answer Incorrect Answer

      Solution

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

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