Nitin borrowed some money at rate of 6% p.a. for first three years, 9% p.a. for next five years and 13% p.a. for period beyond eight years. If total interest paid by him at end of eleven years is Rs. 8160, money borrowed by him (in Rupees) was?

Let the money borrowed by Nitin = Rs. P
According to the question,
$$\eqalign{ & \frac{{{\text{P}} \times 6 \times 3}}{{100}} + \frac{{{\text{P}} \times 9 \times 5}}{{100}} + \frac{{{\text{P}} \times 13 \times 3}}{{100}} = {\text{Rs}}{\text{. }}8160 \cr & \Rightarrow \frac{{{\text{18P}}}}{{100}} + \frac{{{\text{45P}}}}{{100}} + \frac{{{\text{39P}}}}{{100}} = {\text{Rs}}{\text{. 1860}} \cr & \Rightarrow \frac{{{\text{102P}}}}{{100}} = {\text{Rs}}{\text{. 8160}} \cr & \Rightarrow {\text{P = Rs}}{\text{.}}\frac{{8160 \times 100}}{{102}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 8000}} \cr} $$

Alternate
Note : In such type of questions to save your valuable time follow the given below method.
Let principal = Rs. 100
Total Interest
$$\frac{{100 \times 6 \times 3}}{{100}} + \frac{{100 \times 9 \times 5}}{{100}} + $$      $$\frac{{100 \times 13 \times 3}}{{100}}$$
$$\eqalign{ & = 18 + 45 + 39 \cr & = 102{\text{ units}} \cr & {\text{According to the question,}} \cr & {\text{102 units = Rs}}{\text{. 8160}} \cr & {\text{1 unit = Rs}}{\text{. }}\frac{{8160}}{{102}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 80}} \cr & {\text{100 units = Rs}}{\text{. 8000}} \cr & {\text{Hence sum = Rs}}{\text{. 8000}} \cr} $$

Alternate
Total rate of interest in 11 years
$$\eqalign{ & \left( {6 \times 3} \right)\% + \left( {5 \times 9} \right)\% + \left( {3 \times 13} \right)\% {\text{ }} \cr & \Rightarrow 102\% = 8160 \cr & \Rightarrow 100\% = 8000 \cr & \therefore {\text{Sum = Rs}}{\text{. 8000}} \cr} $$