The rate of reduction of a persons assets is proportional to the square root of the existing assets. The assets reduced from 25 lakhs to 6.25 lakhs in 2 years. This rate of reduction of his assets will make him bankrupt in

Step-by-step solution

Assets reduction rate: - dA dt = k A , or dA dt = -k A , with k > 0 . Separate variables: A^ -1/2 dA = -k dt , then integrate both sides. A^ -1/2 dA = -k dt 2 A = -kt + C Initial condition: at t = 0 , A = 25 . So 2 25 = C C = 10 . 2 A = -kt + 10 At t = 2 , A = 6.25 = (2.5)^2 : 2 6.25 = -2k + 10 5 = -2k + 10 k = 2.5 Thus 2 A = -2.5t + 10 . Bankruptcy occurs at A = 0 , so 0 = -2.5t + 10 t = 4 years.