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 the 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?
Let the original rate be R%. Then, new rate = (2R)%.
Note:
Here, original rate is for 1 year(s); the new rate is for only 4 months i.e. $\dfrac{1}{3}$ year(s).
$\therefore \left(\dfrac{725 \times R \times 1}{100} \right) $+$ \left(\dfrac{362.50 \times 2R \times 1}{100 x 3} \right) $= 33.50
$\Rightarrow$ $\left(2175 + 725\right)$ R = 33.50 x 100 x 3
$\Rightarrow$ $\left(2175 + 725\right)$ R = 10050
$\Rightarrow$ $\left(2900\right)$R = 10050
$\Rightarrow$ R =$ \dfrac{10050}{2900} $= 3.46
$\therefore$ Original rate = 3.46%