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:
Answer & explanation
Correct answer: option 3
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