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:

₹10,000

Let initial Rate = R% & Rate after 3 years = ( R  - 2 )%

We know ,

Simple Interest = \(\frac{Principal ×Rate × Time }{100}\)

\(\frac{P ×R× 3 }{100}\) + \(\frac{2P ×(R-2)× 5 }{100}\) = 13600

3RP + 10PR - 20P = 1360000

13PR - 20P = 1360000   ---(1)

Now ,

Time = 11\(\frac{1 }{3}\) =  \(\frac{34 }{3}\)years

13600 =\(\frac{P ×R× 34 }{3×100}\)

PR = 120000   ----(2)

put value of PR into equation 1 .

13 × 120000 - 20P = 1360000

20P = 1560000 - 1360000

P = \(\frac{200000}{20}\)

= 10000