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ATQ, Simple interest = (Sum × rate of interest × time period in years) ÷ 100 So, simple interest earned = {(a + 1000) × 20 × 3} ÷ 100 = Rs. '0.6a + 600' And compound interest earned = (a - 4000) × {1 + (20/100) }3 - (a - 4000) = (a - 4000) × (1.728 - 1) = (a - 4000) × 0.728 = Rs. '0.728a - 2912' So, two cases are possible; Case (I) : simple interest > compound interest So, 0.6a + 600 = 0.728a - 2912 + 1080 Or, 2432 = 0.128a So, a = 19000 Case (II) : simple interest < compound interest So, 0.6a + 600 + 1080 = 0.728a - 2912 Or, 4592 = 0.128a So, a = 35875 For statement I: Since, 'a' can take two values So, statement I is true. For statement II: Again, since 'a' = 19,000 or 35875 which are greater than 10,000 So, statement II is false. For statement III: Since, 'a' has multiple values So, statement III is false.
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