Question

The difference between compound interest (CI) and simple interest (SI) on a sum for $4$ years is \rupee $1282$. Find the sum.
I. Amount of simple interest accrued after $4$ years is \rupee $4000$.
II. Rate of interest is $10\%$ per annum. \bigskip

• A. I alone sufficient; II alone not.
• B. II alone sufficient; I alone not.
• C. Either I alone or II alone sufficient.
• D. Even I + II together not sufficient.
• E. I + II together necessary.
  \bigskip

Hint:

When $r$ is given, CI–SI over multiple years becomes a simple multiplier of $P$. Use it to solve for $P$ directly from the given difference.

Answer 1

The Correct Option is B

For $n=4$ years at rate $r$, the difference (CI$-$SI) equals \[ \Delta = P\!\left[(1+\tfrac{r}{100})^{4} - \Big(1+\tfrac{4r}{100}\Big)\right]. \] With $r=10\%$ (II), $\Delta = P(1.1^4-1.4)=P(1.4641-1.4)=0.0641P$.
Given $\Delta=1282\Rightarrow P=\dfrac{1282}{0.0641}= \rupee \,20000$. So II alone is sufficient.
I alone gives SI (interest) $= \rupee \,4000 = P\cdot \frac{4r}{100}$, but $r$ is unknown $\Rightarrow$ not sufficient. \bigskip