In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and
Give answer
(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 either in statement I alone or in statement II alone are sufficient to answer the question
(D) If the data given in both statements I and II together are not sufficient to answer the question and
(E) If the data in both statements I and II together are necessary to answer the question.
What is the rate of interest?
I.simple interest obtained on the sum of 25000 in 2 years is 250 less than the interest obtained from compound interest during same time
II.simple interest obtained in 10 years is equal to the original sum
Let rate of interest = $$R \%$$
I : P = Rs. 25,000 and time period = 2 years
=> $$S.I. = \frac{P \times R \times T}{100}$$
= $$\frac{25000 \times R \times 2}{100} = 500 R$$
Interest obtained from compound interest = $$P [(1 + \frac{R}{100})^T - 1]$$
=> $$(500R + 250) = 25000 [(1 + \frac{R}{100})^2 - 1]$$
=> $$250 (2R + 1) = 25000 [(1 + \frac{R}{100})^2 - 1]$$
=> $$2R + 1 = 100 (1 + \frac{R^2}{100^2} + \frac{2 R}{100} - 1)$$
=> $$2R + 1 = \frac{R^2}{100} + 2R$$
=> $$R^2 = 100 \times 1 = 100$$
=> $$R = \sqrt{100} = 10 \%$$
Thus, statement I alone is sufficient.
II : Let original sum = simple interest = $$Rs. P$$ and time period = 10 years
=> $$S.I. = \frac{P \times R \times T}{100}$$
=> $$P = \frac{P \times R \times 10}{100}$$
=> $$R = \frac{100}{10} = 10 \%$$
Thus, statement II alone is also sufficient.
Thus, either statement alone is sufficient.
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