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:

Given,

Total Amount = ₹10,000

Let the amount lent at 15% = $$x$$

$$=$$>  Amount lent at 10% = $$10000-x$$

Total interest he received after 5 years amounted to ₹6,500

$$=$$>  $$\frac{x\times15\times5}{100}+\frac{\left(10000-x\right)\times10\times5}{100}=6500$$

$$=$$>  $$\frac{3x}{4}+\frac{1}{2}\left(10000-x\right)=6500$$

$$=$$>  $$\frac{3x}{4}-\frac{x}{2}+5000=6500$$

$$=$$>  $$\frac{3x-2x}{4}=6500-5000$$

$$=$$>  $$\frac{x}{4}=1500$$

$$=$$>  $$x=6000$$

$$\therefore\ $$Difference between the parts of amounts he lent = $$x-\left(10000-x\right)=6000-\left(10000-6000\right)=$$₹ 2000

Hence, the correct answer is Option C