Sameer invested Rs. (R + 1000) at simple interest of 20% p.a. for 3 years. Ajeet invested Rs. (R - 4000) at compound interest of 20% p.a. for 3 years. If the difference between interest earned from both investments is Rs. 1,080, then which of the following statement(s) is/are true?
I. 'R' can take multiple values.
II. The minimum value that 'R' can take is less than 10,000.
III. 'R' must be an even number.
Simple interest = (Sum X rate of interest X time period in years) ÷ 100 So, simple interest earned = {(R + 1000) X 20 X 3} ÷ 100 = Rs. '0.6R + 600' And compound interest earned = (R - 4000) X {1 + (20/100) }3 - (R - 4000) = (R - 4000) X (1.728 - 1) = (R - 4000) X 0.728 = Rs. '0.728R - 2912' So, two cases are possible; Case (I) : simple interest > compound interest So, 0.6R + 600 = 0.728R - 2912 + 1080 Or, 2432 = 0.128R So, R = 19000 Case (II) : simple interest < compound interest So, 0.6R + 600 + 1080 = 0.728R - 2912 Or, 4592 = 0.128R So, R = 35875 For statement I: Since, 'R' can take two values So, statement I is true. For statement II: Again, since 'R' = 19,000 or 35875 which are greater than 10,000 So, statement II is false. For statement III: Since, 'R' has multiple values So, statement III is false.
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