Question

A sum of $Rs.725$ is lent in the beginning of a year at a certain rate of interest. After $8$ months a sum of $Rs.362.50$ more is lent, but at a rate twice the former. At the end of the year $Rs.33.50$ is earned as interest from both the loans. What was the original rate of interest ?

• A. $4.5\%$
• B. $3.6\%$
  
• C. $3.46\%$
• D. $2.47\%$

Answer 1

Answer: (C)

$3.46\%$

Let the original rate be $R\%$. Then, new rate $=\left(2R\right)\%$.

Note:
Here, original rate is for $1$ year(s); the new rate is for only $4$ months i.e. $\frac{1}{3}$year(s).

$\therefore \left(\frac{725\times R\times 1}{100}\right)+\left(\frac{362.5\times 2R\times 1}{100\times 3}\right)=33.50$

$\Rightarrow (2175+725)R=33.50\times 100\times 3$

$\Rightarrow (2175+725)R=10050$

$\Rightarrow \left(2900\right)R=10050$

$\Rightarrow R=\frac{10050}{2900}=3.46$

	Therefore, original rate is $3.46\%$.