Question

A sum at a simple interest of $12\frac{1}{2}$% amounts to $Rs.2,502.50$ after $3$ years. Find the sum, and the interest

Answer 1

Given: $Amount=Rs.2,502.50$, and $R=12\frac{1}{2}$% $=\frac{25}{2}$%. Let sum be x. Using the formula, we have
$I=\frac{PTR}{100}=\frac{x\times 3\times 25}{2\times 100}=\frac{75x}{200}=\frac{3x}{8}$.
But we know that
$Amount=Principal+Simpleinterest=x+\frac{3x}{8}=\frac{(8x+3x)}{8}=\frac{11x}{8}$.
Solving for x, we get
$x=\frac{2502.5\times 8}{11}=1820$.
Hence, the sum is $Rs.1,820$. The interest is
$Rs.2,502.50-Rs.1,820=Rs.682.50$.