Ashish borrowed a sum of money from a nationalised bank at 12\% simple interest per annum and the same amount at $10 \%$ simple interest per annum both for the same period. He cleared the first loan 6 months before the scheduled date of repayment and repaid the second loan just at the end of the scheduled period. If in each case he had to pay ₹ 3250 as amount then how much and for what time did he borrow? (P.C.S., 2006)
Answer
Answer (as printed):
Explanation
Let each sum $=₹ x$. Let first sum be invested for $T$ years and the second sum for $\left(T-\frac{1}{2}\right)$ years. $$\text { Then, } x+\frac{x \times 12 \times\left(T-\frac{1}{2}\right)}{100}=3250$$ $$\begin{aligned} & \Rightarrow \quad 100 x+12 x T-6 x=3250000 \\ & \Rightarrow \quad 94 x+12 x T=32500 \end{aligned}$$ $$\text { And, } \quad x+\frac{x \times 10 \times T}{100}=3250 \Rightarrow 100 x+10 x T=325000$$ From (i) and (ii), we get: $94 x+12 x T=100 x+10 x T \Rightarrow 6 x=2 x T$ $$\Rightarrow \quad 2 T=6 \Rightarrow T=3 .$$ Putting $T=3$ in (i), we get: $94 x+36 x=325000 \Rightarrow 130 x=325000 \Rightarrow x=2500$.
Explanation as extracted from the printed page; notation may be imperfect.