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 ₹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:

Let the principal amount = P

Rate of interest = R

According to the question

$$\frac{P\times3\times R}{100}+\frac{2P\times5\times\left(R-2\right)}{100}=13600$$

$$=$$>  $$\frac{3PR}{100}+\frac{10PR}{100}-\frac{20P}{100}=13600$$

$$=$$>  $$\frac{13PR}{100}-\frac{20P}{100}=13600$$ .............(1)

Given, interest on P after $$11\frac{1}{3}$$ years at the rate of R% = ₹ 13,600

$$=$$>  $$\frac{P\times\frac{34}{3}\times\ R}{100}=13600$$

$$=$$>  PR = 120000

Substituting PR = 120000 in equation (1)

$$\frac{13\times120000}{100}-\frac{20P}{100}=13600$$

$$=$$>  $$15600-\frac{P}{5}=13600$$

$$=$$>  $$\frac{P}{5}=15600-13600$$

$$=$$>  $$\frac{P}{5}=2000$$

$$=$$>  P = 10000

$$\therefore\ $$Loan taken initially = ₹ 10,000

Hence, the correct answer is Option D