Vaishali invested Rs. (X + 3000) on compound interest of r% p.a. compounded annually for 2 years and Tanushi invested Rs. (X – 2000) on simple interest of (r – 2)% p.a. for 3 years. The total interest received by both of them is together Rs. 12360. If Anuj invested Rs. (X + 8000) on simple interest for 3 years on 15% and received an interest of Rs. 13500, find the value of ‘r’.

According to the question, Simple interest received by Anuj = Rs. 13500 (X + 8000) × 15% × 3 = 13500 (X + 8000) = 30000 X = 22000 Amount invested by Vaishali = Rs. 22000 + 3000 = Rs. 25000 Amount invested by Tanushi = 22000 – 2000 = Rs. 20000 The total interest received by Vaishali and Tanushi = 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