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# 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.

a

If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.

b

If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.

c

If the data in Statement I alone or in Statement II alone are sufficient to answer the question.

d

If the data in both the Statements I and II are not sufficient to answer the question.

e

If the data in both the Statements I and II together are necessary to answer the question.

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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