What is the rate of interest?

I. Simple interest accrued on an amount of Rs. 25,000 in two years is less than the compound interest for the same period by Rs. 250.

II. Simple interest accrued in 10 years is equal to the principal.

Answer : Option C

Explanation : From statement II,

If principal = Rs. *x*, then interest after 10 years = Rs. *x *

$herefore x = frac{{x imes { m{Rate}} imes 10}}{{100}}$

$Rightarrow$ Rate = 10% p.a.

From statement I,

Principal = $frac{{{ m{Difference}} imes {{(100)}^2}}}{{{{({ m{Rate}})}^2}}}$

$Rightarrow 25000 = frac{{250 imes {{(100)}^2}}}{{{{({ m{Rate}})}^2}}}$

$Rightarrow {({ m{Rate}})^2} = frac{{250 imes 10000}}{{25000}} = 100$

$Rightarrow { m{Rate}} = sqrt {100} = 10{ m{\% p}}.{ m{a}}$

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