Vishwas borrowed a total amount of ₹ 30000, part of it on simple interest rate of 12 p.c.p.a. and remaining on simple interest rate of 10 p.c.p.a. If at the end of 2 years he paid in all ₹ 36480 to settle the loan amount, what was the amount borrowed at 12 p.c.p.a? (Bank P.O., 2008)

### Concept & Logic This is a mixture/allocation problem that can be solved using basic linear equations or the method of alligation. $$\text{Total Interest} = SI_1 + SI_2$$ ### Step-by-Step Solution * **Given:** Total Principal = ₹ 30,000. Total Amount paid = ₹ 36,480. Time = 2 years. * Total Interest for 2 years = $36,480 - 30,000$ = ₹ 6,480. * Interest per year = $\frac{6480}{2}$ = ₹ 3,240. * Let the amount borrowed at 12% be $x$. Then, the amount borrowed at 10% is $(30000 - x)$. * **Calculation:** $$x \times 12\% + (30000 - x) \times 10\% = 3240$$ $$0.12x + 3000 - 0.10x = 3240$$ $$0.02x = 240$$ $$x = \frac{240}{0.02} = 12000$$ * The amount borrowed at 12% is ₹ 12,000. ### Exam Strategy & Shortcut Use Alligation on the interest rate. Overall rate for 1 year = $\frac{3240}{30000} \times 100 = 10.8\%$. Part 1 (12%) | Part 2 (10%) \ | / 10.8% / | \ (10.8 - 10) = 0.8 | (12 - 10.8) = 1.2 Ratio of sums = $0.8 : 1.2 = 2 : 3$. Amount at 12% = $\frac{2}{5} \times 30000 = 12000$. ### Common Pitfall A common mistake is using the 2-year total interest (₹ 6,480) in the 1-year equation without dividing it by 2, which leads to incorrect calculations and mismatched answers. ### Final Answer Therefore, the correct answer is **₹ 12000**.