Multiple choice

Find the simple interest of 4 years and 5 months- Statement I: Ratio of SI and CI on principal for 2 years is 75:84. Statement II: Compound interest of 1 year and 6 months is 2430 Rs. Statement III: Compound interest of 2 years is 53.76% of the principal itself.

  1. Any two are sufficient

  2. II and (I or III) together are sufficient

  3. Only II and III together are sufficient

  4. All three together are sufficient

  5. Other than given options
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement III: CI of 2 years = 53.76% of principal. Using CI formula: P(1+r)² - P = 0.5376P, giving (1+r)² = 1.5376, so 1+r = 1.24, r = 24%. Statement II: CI for 1.5 years at 24% = P[(1.24)^1.5 - 1] = 2430, giving P = Rs 10000. Statement I: SI:CI ratio for 2 years is 75:84. At 24%, SI(2y) = 48%, CI(2y) = 53.76%. Ratio 48:53.76 simplifies to 75:84 (true). So I is redundant. II and III are sufficient. II gives P, III gives r. SI for 4y 5m = 10000 × 0.24 × (53/12) = Rs 10600. Option B is correct.

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