A man has Rs. 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 amount to Rs. 6,500. The difference between the parts of the amounts he lent is:

Solution (By Examveda Team)

$$\eqalign{ & {\bf{Given,}} \cr & {\text{Principal}} = {\text{Rs}}{\text{. }}10,000 \cr & {\text{Some part of money lent at }}15\% \cr & {\text{Some part of it lent at }}10\% \cr & {\text{Total interest earned}} = {\text{Rs}}{\text{. }}6,500 \cr & {\text{Time}} = 5{\text{ years}} \cr & {\bf{Formula}}\,{\bf{used:}} \cr & {\text{Interest}} = \frac{{{\text{Principal}} \times {\text{Rate}} \times {\text{Time}}}}{{100}} \cr & {\bf{Calculation:}} \cr & {\text{Let the money lent at }}15\% {\text{ be }}x \cr & {\text{Then money lent at }}10\% {\text{ be }}\left( {10,000 - x} \right) \cr & 6,500 = \frac{{x \times 15 \times 5}}{{100}} + \frac{{\left( {10,000 - x} \right) \times 10 \times 5}}{{100}} \cr & \Rightarrow 6,500 = \frac{{3x}}{4} + \frac{{10,000 - x}}{2} \cr & \Rightarrow 6,500 = \frac{{3x + 20,000 - 2x}}{4} \cr & \Rightarrow 26,000 = 20,000 + x \cr & \Rightarrow x = {\text{Rs}}{\text{. }}6,000 \cr & {\text{Then,}} \cr & \left( {10,000 - x} \right) = \left( {10,000 - 6,000} \right) = {\text{Rs}}{\text{. }}4000 \cr & {\text{Difference between the two sums lent}} \cr & = {\text{Rs}}{\text{. }}6,000 - {\text{Rs}}{\text{. }}4,000 \cr & = {\text{Rs}}{\text{. }}2,000 \cr & \therefore {\text{The difference between the sums lent is Rs}}{\text{. }}2,000 \cr} $$