Investor V placed Rs. (a + 3000) in a compound interest account with an annual interest rate of r%, compounded annually for a span of 2 years. Simultaneously, investor T invested Rs. (a – 2000) in a simple interest account with an interest rate of (r – 2)% p.a. for a duration of 3 years. The cumulative interest earned by both investors amounted to Rs. 12360. Additionally, investor A contributed Rs. (a + 8000) in a simple interest account with a 15% interest rate for 3 years, accumulating an interest of Rs. 13500. The enigma to unravel is the value of 'r'.

According to the question, Simple interest received by A = Rs. 13500 (a + 8000) × 15% × 3 = 13500 (a + 8000) = 30000 a = 22000 Amount invested by V = Rs. 22000 + 3000 = Rs. 25000 Amount invested by T = 22000 – 2000 = Rs. 20000 The total interest received by V and T = Rs. 12360 [25000 × (1 + r/100)² – 25000] + [20000 × (r – 2)% × 3] = 12360 25000 × (1 + r/100)² – 25000 + 600(r – 2) = 12360 25000 × (1 + r²/10000 + r/50) – 25000 + 600(r – 2) = 12360 25000 + 2.5r² + 500r – 25000 + 600(r – 2) = 12360 2.5r² + 500r + 600r – 1200 = 12360 2.5r² + 1100r = 13560 r² + 440r – 5424 = 0 r² + 452r – 12r – 5424 = 0 r(r + 452) – 12(r + 452) = 0 (r + 452)(r – 12) = 0 r = -452, 12 Rate of interest cannot be negative. So, r = 12