A man takes a loan of some amount at some rate of simple interest. After three years, the loan amount is doubled and rate of interest is decreased by 2%. After 5 years, if the total interest paid on the whole is Rs. 13,600, which is equal to the same when the first amount was taken for $$11\frac{1}{3}$$ years, then the loan taken initially is:

Solution(By Examveda Team)

$$\eqalign{ & \frac{{x \times r \times 3}}{{100}} + \frac{{2x \times \left( {r - 2} \right)}}{{100}} \times 5 = \frac{{x \times r}}{{100}} \times \frac{{34}}{3} \cr & \frac{{2x \times \left( {r - 2} \right) \times 5}}{{100}} = \frac{{x \times r}}{{100}} \times \frac{{34}}{3} - \frac{{x \times r \times 3}}{{100}} \cr & \frac{{2x \times \left( {r - 2} \right) \times 5}}{{100}} = \frac{{\left( {34r - 9r} \right) \times x}}{{300}} \cr & 6\left( {r - 2} \right) \times 5 = 25r \cr & \frac{{36x}}{{100}} + \frac{{2x \times 10}}{{100}} \times 5 = 13600 \cr & \frac{{136x}}{{100}} = 13600 \cr & x = {\text{Rs}}{\text{. }}10000 \cr} $$