The questions given below contain two statements numbered I and II giving certain data. You have to decide whether the data given in the statements are sufficient to answer the question. Give answer
Gaurav invested a certain sum in scheme A, which offers compound interest (compounded annually). What is the rate of interest offered by scheme A (in pcpa)? I
The sum invested by Gaurav amounted to 12240 in 2 years.
II The sum invested by Gaurav amounted to 14688 in three years.

Options

A. if statement I alone is sufficient but statement II alone is not sufficient.
B. if statement II alone is sufficient but statement I alone is not sufficient.
C. if either statement I or II is sufficient.
D. if both statement I and II together are suficient, but neither of them alone is sufficient.

Answer

To determine the rate of interest offered by scheme A, we need to analyze the two statements provided.

### Step-by-step Solution:

1. **Understanding the Problem**: We need to find the rate of interest (R) for a compound interest scheme. The amount after a certain period is given in both statements.

2. **Statement I Analysis**:
- The first statement tells us that the amount after 2 years is 12,240.
- The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
where:
- \(A\) = Amount after time \(T\)
- \(P\) = Principal amount (initial investment)
- \(R\) = Rate of interest
- \(T\) = Time in years
- Here, we have:
\[ 12240 = P \left(1 + \frac{R}{100}\right)^2 \]
- Since we have two unknowns (P and R), we cannot solve for R using this statement alone.

3. **Statement II Analysis**:
- The second statement tells us that the amount after 3 years is 14,688.
- Using the same formula:
\[ 14688 = P \left(1 + \frac{R}{100}\right)^3 \]
- Again, we have two unknowns (P and R) and cannot find R using this statement alone.

4. **Combining Both Statements**:
- Now, if we consider both statements together, we have:
1. \(12240 = P \left(1 + \frac{R}{100}\right)^2\) (from Statement I)
2. \(14688 = P \left(1 + \frac{R}{100}\right)^3\) (from Statement II)
- We can solve these two equations simultaneously to find the values of P and R.

5. **Conclusion**:
- Since neither statement alone is sufficient to determine the rate of interest, but together they provide enough information to solve for R, the answer is that both statements together are sufficient.

### Final Answer:
The answer is option 4: Both statements are sufficient, but neither statement alone is sufficient.