The assets of a person reduced in his business such that the rate of reduction is proportional to the square root of the existing assets. If the assets were initially ₹ 10 lakhs and due to loss they reduce to ₹ 10000 after 3 years, then the number of years required for the person to be bankrupt will be

Step-by-step solution

If A denotes the assets at time t , the rate of reduction is proportional to A , so dA dt = -k A Separating and integrating gives A^ -1/2 ,dA = -k ,dt 2 A = -kt + C At t = 0 , A = 10^6 , hence 2 10^6 = C , so C = 2000 . At t = 3 , A = 10^4 , giving 2 10^4 = -3k + 2000 200 = -3k + 2000 k = 600 The solution becomes 2 A = -600t + 2000 . Set A = 0 for bankruptcy: 0 = -600t + 2000 , so t = 2000 600 = 10 3 years. Correct choice is B.