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) B 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 $n=1,A=Rs1100$
$\therefore R=10$ %
Hence, C.l. after 3 years can be calculated.
$\therefore$ Statement (I) alone is sufficient to answer the question.
Now, since difference between S.l. and C.I. for 2 years $=P\times {\left(\frac{R}{100}\right)}^2$
$\therefore$ 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.