Arun borrowed a sum of money from Jayant at the rate of 8% per annum simple interest for the first four years, 10% per annum for the next 6 years and 12% per annum for the period beyond 10 years. If he pays a total of Rs. 12160 as interest only at the end of 15 years, how much money did he borrow?
Correct Answer: Rs. 8000
$$\eqalign{ & {\text{Let the sum be Rs}}{\text{. }}x \cr & {\text{Then,}} \cr} $$
$$ {\frac{{x \times 8 \times 4}}{{100}}} + {\frac{{x \times 10 \times 6}}{{100}}} \,+ $$ $$ {\frac{{x \times 12 \times 5}}{{100}}} $$ $$ = 12160$$
$$\eqalign{ & \Rightarrow 32x + 60x + 60x = 1216000 \cr & \Rightarrow 152x = 1216000 \cr & \Rightarrow x = 8000 \cr} $$
$$ {\frac{{x \times 8 \times 4}}{{100}}} + {\frac{{x \times 10 \times 6}}{{100}}} \,+ $$ $$ {\frac{{x \times 12 \times 5}}{{100}}} $$ $$ = 12160$$
$$\eqalign{ & \Rightarrow 32x + 60x + 60x = 1216000 \cr & \Rightarrow 152x = 1216000 \cr & \Rightarrow x = 8000 \cr} $$