Question

What was the total compound interest on a sum after three years?
I. The simple 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/-

• A. Data in the statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
• B. 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. Data either in statement I alone or in statement II alone are sufficient to answer the question.
• D. Data given in both the statements I and II together are not sufficient to answer the question.
• E. Data in both the statements I and II together are necessary to answer the question.

Answer 1

The correct option is C Data either in statement I alone or in statement II alone are sufficient to answer the question.

From the statement I.
$r=\frac{100\times 100}{1000}=10\%$
Thus we have,
$P=Rs.1000,r=10\%,t=3years$
Hence, C.I. can be determined
From the statement II.
$S.I.=\frac{1000\times r\times 2}{1000}=20rC.I.=1000[{(1+\frac{r}{100})}^2-1]$
$\therefore C.I.-S.I.=1000\left[\frac{200r+r^2}{10000}\right]-20r\Rightarrow 2000r+r^2-200r=100\Rightarrow r=10$
Hence, C.I. can be determined.