Multiple choice

Find the correct relationship between given quantities. Q1: 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? Q2: 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. Q1 > Q2

  2. Q1 ≥ Q2

  3. Q1 < Q2

  4. Q1 ≤ Q2

  5. Q1 = Q2 or relationship cannot be established
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A Correct answer
Explanation

For CI-SI difference over 2 years: Difference = P[(1+R/100)² - 1 - 2R/100] = P(R/100)². Therefore P = Difference × (100/R)². For Q1: P1 = 100 × (100/9)² = 100 × 123.46 = 12346 (approx). For Q2: P2 = 97 × (100/11)² = 97 × 82.64 = 8016 (approx). Since 12346 > 8016, Q1 > Q2.

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