'S' undertook an investment endeavor by allocating a capital denoted as 'a + 1000' into a scheme yielding a straightforward interest rate of 20% per annum for a duration of three years. Simultaneously, 'A' ventured into a financial enterprise involving an amount 'a - 4000' invested in a compound interest scheme at a 20% annual rate for a three-year period.If the difference between interest earned from both investments is Rs. 1,080, Determine then which of the following statement(s) is/are true?

I. The variable 'a' can take multiple values.

II. The minimal admissible value for 'a' proves to be less than the grand threshold of 10,000.

III. 'a' is compelled to be an integer of even number."

Solution

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.