A sum of money amounts to Rs 5400 in 3 years and to Rs 6000 in 5 years at simple interest. Find the principal and the rate of interest per annum.

Let principal = P, rate = r% per annum. Amount after 3 years = P + SI₃ = 5400 Amount after 5 years = P + SI₅ = 6000 Difference in amount for 2 extra years: SI for 2 years = 6000 − 5400 = 600 At SI, interest is same each year: Interest for 1 year = 600 / 2 = 300 So, using SI formula: SI(1 year) = P × r × 1 / 100 = 300 ⇒ P×r = 30000 …(i) Also, SI for 3 years = 3 × 300 = 900 So P + 900 = 5400 ⇒ P = 5400 − 900 = 4500 From (i): 4500 × r = 30000 ⇒ r = 30000 / 4500 = 20/3 %  Answer: Principal = Rs 4500, Rate = 20/3 % per annum.