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. $1000$.
(II) The difference between simple and compound interest on a sum of Rs. $1000$ at the end of two years was Rs. $10$.

• A. Statement (I) alone is sufficient, but statement (II) alone is not sufficient.
• B. Statement (II) alone is sufficient, but statement (I) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.

Answer 1

The correct option is D Each statement alone is sufficient.

$\because Amount=P(1+\frac{R}{100}{)}^n$
(I) $\Rightarrow$ For $P=1000$ and $n=1,A=Rs.1100$
$\therefore R=10$%
Hence, C.I. after $3$ years can be calculated.
$\therefore$ Statement (I) alone is sufficient to answer the question.
Now, since difference between S.I. and C. I. for $2$ years $=P\times (\frac{R}{100}{)}^2$
$\therefore$ From (II), R can be calculated.
Hence, C.I. after $3$ years can be determined.
Therefore, each statement alone is sufficient to answer the question.