A man has ₹10,000. He lent a part of it at 15% simple interest and the remaining at 10% simple interest. The total interest he received after 5 years amounted to ₹6,500. The difference between the parts of the amounts he lent is:

₹2,000

Let sum lent at 15% be P .

We know ,

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

6500 = \(\frac{P × 15 × 5 }{100}\) + \(\frac{(10000-P) × 10 × 5 }{100}\) 

6500 = \(\frac{3P }{4}\) + \(\frac{(10000-P)  }{2}\)

26000 = 3P + 20000 - 2P

P = 6000

Another amount = ( 10000 - 6000 ) = 4000

Required difference b/w the both sums = 6000 - 4000 = Rs. 2000