Question

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

• 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.

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  

\[\Delta = P \left[ \left(1 + \tfrac{r}{100}\right)^4 - \left(1 + \tfrac{4r}{100}\right) \right].\]

With $r = 10\%$ (II),  
\[\Delta = P(1.1^4 - 1.4) = P(1.4641 - 1.4) = 0.0641P.\]

Given $\Delta = 1282 \Rightarrow P = \tfrac{1282}{0.0641} = \text{₹}\,20000.$  
So II alone is sufficient.  

I alone gives SI (simple interest) = ₹4000 = $P \cdot \tfrac{4r}{100}$, but $r$ is unknown $\Rightarrow$ not sufficient.