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      Question

      The following questions each present two quantities,

      Quantity I and Quantity II. Compare the values of the two quantities and determine their relationship. Quantity I:  P deposits ₹6500 at compound interest for 3 years at an annual rate of r%. After 3 years, the total amount he receives is ₹8651.5. Determine the value of r. Quantity II : R borrows ₹70,000 from a bank at 10% simple interest per year. At the same time, he lends this entire amount to his friend Q at a simple interest rate of (r + 5)% per year. After 3 years, his total gain is ₹10,000. Determine the value of r.
      A Quantity > Quantity II Correct Answer Incorrect Answer
      B Quantity < 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: Principal = Rs.6500 Rate of interest = r% According to the question, 6500 × (1+ r/100)³ = 8651.5 (1 + r/100)³ = 8651.5/6500 (100 + r)³ = 1.331 × (100)³ r = 10% Quantity II: Principal = Rs.70,000 Interest paid by 'R' to bank = (70000×10×3)/100 = Rs.21000 Still he got Rs.10000 as a profit That means the interest paid by Q is 21000 + 10,000 = Rs.31000 31000/70000 = 44.28% For 1year, interest rate = 44.28/3 = 14.76% r = 14.76 - 5 = 9.76%

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