In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum?

1 $1 \frac{1}{4}$ $1\frac{1}{4}$ years
2 $1 \frac{3}{4}$ $1\frac{3}{4}$ years
3 $2 \frac{1}{4}$ $2\frac{1}{4}$ years
4 $2 \frac{3}{4}$ $2\frac{3}{4}$ years

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let sum = x . \\ Then, \\ S .I . = 0.125 x = \frac{1}{8} x \\ R = 10 % \\ ∴ R a t e \\ = (\frac{100 \times x}{x \times 8 \times 10}) years \\ = \frac{5}{4} years \\ = 1 \frac{1}{4} years \end{aligned}

$\eqalign{ & {\text{Let sum}} = x. \cr & {\text{Then,}} \cr & {\text{S}}{\text{.I}}{\text{.}} = 0.125x = \frac{1}{8}x \cr & {\text{R}} = 10\% \cr & \therefore Rate \cr & = \left( {\frac{{100 \times x}}{{x \times 8 \times 10}}} \right){\text{years}} \cr & = \frac{5}{4}{\text{years}} \cr & = {\text{1}}\frac{1}{4}{\text{years}} \cr}$