A person lends out ₹ 9000 on the condition that the loan is payable in 10 months by 10 monthly equal instalments of ₹ 1000 each. Find the rate of simple interest charged. (S.S.C., 2006)
Answer
Answer (as printed):
Explanation
We have: ₹ 9000 + S.I. on ₹ 9000 for 10 months $$=₹ 10000+\text { S.I. on } ₹ 1000 \text { for }(1+2+\ldots+9) \text { months. }$$ $$\begin{aligned} \Rightarrow & ₹ 9000+\text { S.I. on } ₹ 1000 \text { for } 90 \text { months } \\ & =₹ 10000+\text { S.I. on } ₹ 1000 \text { for } 45 \text { months } \end{aligned}$$ $$\begin{aligned} & \Rightarrow \quad \text { S.I. on ₹ } 1000 \text { for } 45 \text { months }=₹ 1000 . \\ & \therefore \quad \text { Rate }=\left(\frac{100 \times 1000 \times 12}{1000 \times 45}\right) \%=\frac{80}{3} \%=26 \frac{2}{3} \% . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.