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

a) $$1\frac{1}{4}$$ years
b) $$1\frac{3}{4}$$ years
c) $$2\frac{1}{4}$$ years
d) $$2\frac{3}{4}$$ years

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

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