Multiple choice

Two quantities that is I and II are given in following questions. Students is expected to solve the quantities and answer them according to given options by comparing their numerical values. Quantity I: Two equal amounts are invested for 2 years at 9% per annum by Anushika, one at simple interest and the other at compound interest. If the difference in the interests for the two years on the two amounts is 100, then what is the amount? Quantity II: Two equal amounts are invested for 2 years at 11% per annum by Anushika, one at simple interest and the other at compound interest. If the difference in the interests for the two years on the two amounts is 97, then what is the amount?

  1. Quantity I > Quantity II

  2. Quantity I ≤ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I ≥ Quantity II

  5. Quantity I = Quantity II or relation can’t be established.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: For 2 years at 9%, difference between CI and SI on amount P is P × (9/100)² × (2 + 9/100) = P × 0.081 × 2.09 ≈ 0.1693P. Given difference is 100, so P ≈ 100/0.1693 ≈ 5907. Quantity II: For 2 years at 11%, difference is P × (11/100)² × 2.22 ≈ 0.2686P. Given difference is 97, so P ≈ 97/0.2686 ≈ 3612. Clearly, Quantity I (5907) > Quantity II (3612), making option A correct.

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