Multiple choice

Passage

Directions: In the following item, quantity I and quantity II are given. Determine the relationship between the quantities and choose the appropriate option. (1) If Quantity I ≥ Quantity II (2) If Quantity I > Quantity II (3) If Quantity I < Quantity II (4) If Quantity I = Quantity II or the relationship cannot be established from the information given (5) If Quantity I ≤ Quantity II

Ravi took a loan of Rs. X from bank A and Rs. 2X from bank B, each for 2 years. Bank A charges simple interest per annum. Bank B charges compound interest per annum at the rate of 10% per annum. The respective ratio between the interest from bank A and that from bank B was 5 : 14. Quantity I: Rate of interest charged by bank A Quantity II: Rate of interest charged by bank C when Rs. 1600 is borrowed by Ravi for 3 years gives simple interest of Rs. 408

  1. (1)

  2. (2)

  3. (3)

  4. (4)

  5. (5)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Bank A interest = X * R * 2 / 100. Bank B interest = 2X * ((1.1)^2 - 1) = 2X * 0.21 = 0.42X. Ratio A:B = (0.02*X*R) / (0.42*X) = 5/14. (0.02*R)/0.42 = 5/14. R = (5 * 0.42) / (14 * 0.02) = 2.1 / 0.28 = 7.5%. Quantity II: 408 = 1600 * R * 3 / 100 => 408 = 48 * R => R = 8.5%. Since 7.5 < 8.5, Q1 < Q2.

AI explanation

The interest from Bank B on principal 2X at 10% compound interest for 2 years is 2X(1.1^2 - 1) = 0.42X. The simple interest from Bank A is (X * Rate * 2) / 100, and the given ratio of interests is 5:14, making the equation [(X * Rate * 2) / 100] / 0.42X = 5/14. Solving this yields Rate = 7.5%, which is Quantity I. The simple interest formula for Bank C gives Quantity II as (1600 * Rate * 3) / 100 = 408, meaning the rate is 8.5% and Quantity II is 8.5. Since 7.5% is less than 8.5%, Quantity I < Quantity II.

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