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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 the question and 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.
Give answer b: if the data in statement H alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
Give answer c: if the data either in statement I alone or in statement II alone are sufficient to answer the question.
Give answer d: if the data even in both the statements I and H together are not sufficient to answer the question.
Give answer e: if the data in both the statements I and II together are necessary to answer the question.
What was the total compound interest on a sum after three years
I. The interest after one year was Rs. 100/- and the sum was Rs. 1,000/-
II. The difference between simple and compound interest on a sum of Rs. 1,000/- at the end of two years was Rs. 10/-.
C.I. = $$P [(1 + \frac{R}{100})^T - 1]$$
I : Interest = 100 and sum = 1000 and time = 1 year
=> $$100 = 1000 [(1 + \frac{R}{100})^1 - 1]$$
=> $$\frac{100}{1000} = [(1 + \frac{R}{100}) - 1]$$
=> $$\frac{R}{100} = \frac{1}{10}$$
=> $$R = \frac{100}{10} = 10 \%$$
$$\therefore$$ C.I. after 3 years = $$1000 [(1 + \frac{10}{100})^3 - 1]$$
= $$1000 [(\frac{11}{10})^3 - 1]$$
= $$1000 [\frac{1331}{1000} - 1] = 1000 \times \frac{331}{1000}$$
= $$331$$
Thus, I alone is sufficient.
II : Sum = 1000 , rate = $$R \%$$
S.I. after 2 years = $$\frac{P \times R \times T}{100}$$
= $$\frac{1000 \times R \times 2}{100} = 20R$$
C.I. after 1st year = $$\frac{R}{100} \times 1000 = 10R$$
C.I. after 2nd year = $$10R + \frac{R}{100} \times 10R = 10R + \frac{R^2}{10}$$
=> Required difference = 10
=> $$(10R + 10R + \frac{R^2}{10}) - (20R) = 10$$
=> $$\frac{R^2}{10} = 10$$
=> $$R^2 = 10 \times 10 = 100$$
=> $$R = \sqrt{100} = 10 \%$$
$$\therefore$$ C.I. after 3 years = $$1000 [(1 + \frac{10}{100})^3 - 1]$$
= $$1000 [(\frac{11}{10})^3 - 1]$$
= $$1000 [\frac{1331}{1000} - 1] = 1000 \times \frac{331}{1000}$$
= $$331$$
Thus, II alone is sufficient.
Thus, either statement alone is sufficient.
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