A sum of ₹ 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of ₹ 362.50 more is lent but at the rate twice the former. At the end of the year, ₹ 33.50 is earned as interest from both the loans. What was the original rate of interest ?
(a)3.6\%
(b)4.5\%
(c)5\%
(d)6\%
(e)None of these
Answer
Answer (as printed): E
Explanation
Let the original rate be R\%. Then, new rate $=(2 R) \%$. $$\begin{aligned} & \therefore \quad\left(\frac{725 \times R \times 1}{100}\right)+\left(\frac{362.50 \times 2 R \times 1}{100 \times 3}\right)=33.50 \\ & \Leftrightarrow \quad(2175+725) R=33.50 \times 100 \times 3=10050 \\ & \Leftrightarrow \quad R=\frac{10050}{2900}=3.46 . \\ & \therefore \quad \text { Original rate }=3.46 \% . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.