Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. (Only quantity is to be considered) Find the principal . Quantity I :- If the difference between compound interest and simple interest at 12 % per annum in 2 years is 1296 . Quantity II :- If the compound interest of two years, at the rate in which a sum of Rs 512 becomes Rs 729 in 3 years , is Rs 21250 .

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or relation can't be established
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A Correct answer
Explanation

Quantity I: CI - SI difference formula for 2 years at r% is P × (r/100)². Given 1296 = P × (12/100)² = P × 0.0144, so P = 1296/0.0144 = Rs 90,000. Quantity II: Rs 512 becomes Rs 729 in 3 years. Growth factor = 729/512 = (9/8)³ = 1.4238, meaning annual rate = 12.5%. CI for 2 years at 12.5% on principal P: P × [(1.125)² - 1] = 21250. So P × 0.265625 = 21250, giving P = Rs 80,000. Since 90,000 > 80,000, Quantity I > Quantity II.

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