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

Step 1: Using Statement II's rate \( r=10\% \), the standard \( 4 \)-year difference formula gives \[ D_4=P\left[(1.1)^4-1-0.4\right]=P(1.4641-1.4)=0.0641P. \]

Step 2: Given \( D_4=₹1282 \), solve \[ P=\frac{1282}{0.0641}=₹20{,}000. \]

Step 3: Statement I alone only gives \( SI=P\cdot\tfrac{4r}{100}=₹4000 \), a single equation with two unknowns \( P \) and \( r \), which cannot be solved alone.
\[ \boxed{\text{II alone sufficient}} \]