Each of the questions given below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements sufficient to answer the question. Read both the statements and give answer:
Sussane invested a certain sum in scheme A which offers compound interest (compounded annually). What is the rate of interest offered by scheme A?
I. The sum invested by Sussane a amounted to Rs 7488 in 2 years.
II. The sum invested by Sussane amounted to rs8985.60 in 3 years.

Options

A. if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
B. if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
C. if the data in statement I alone or in statement II alone are sufficient to answer the question.
D. if the data in both the statements I and II together are sufficient to answer the question.

Answer

To determine the rate of interest offered by scheme A based on the information provided in the statements, we can follow these steps:

### Step 1: Understand the Problem
We need to find the rate of interest (R) for a compound interest scheme given two statements about the amount invested and the total amount after certain years.

### Step 2: Analyze Statement I
- **Statement I**: The sum invested by Sussane amounted to Rs 7488 in 2 years.
- Using the formula for compound interest:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Here, \(A = 7488\), \(T = 2\), and \(P\) is unknown.

Rearranging gives:
\[ 7488 = P \left(1 + \frac{R}{100}\right)^2 \]

We have one equation with two unknowns (P and R), which is insufficient to solve for R.

### Step 3: Analyze Statement II
- **Statement II**: The sum invested by Sussane amounted to Rs 8985.60 in 3 years.
- Again, using the compound interest formula:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Here, \(A = 8985.60\), \(T = 3\), and \(P\) is unknown.

Rearranging gives:
\[ 8985.60 = P \left(1 + \frac{R}{100}\right)^3 \]

Similar to Statement I, we have one equation with two unknowns (P and R), which is also insufficient to solve for R.

### Step 4: Combine Both Statements
Now, we will combine the information from both statements:
1. From Statement I:
\[ 7488 = P \left(1 + \frac{R}{100}\right)^2 \quad \text{(1)} \]
2. From Statement II:
\[ 8985.60 = P \left(1 + \frac{R}{100}\right)^3 \quad \text{(2)} \]

### Step 5: Solve the Equations
We can divide Equation (2) by Equation (1):
\[ \frac{8985.60}{7488} = \frac{P \left(1 + \frac{R}{100}\right)^3}{P \left(1 + \frac{R}{100}\right)^2} \]
This simplifies to:
\[ \frac{8985.60}{7488} = 1 + \frac{R}{100} \]
Calculating the left side:
\[ \frac{8985.60}{7488} \approx 1.199 \]
Thus, we have:
\[ 1.199 = 1 + \frac{R}{100} \]
Subtracting 1 from both sides:
\[ 0.199 = \frac{R}{100} \]
Multiplying by 100 gives:
\[ R = 19.9 \]

### Conclusion
The rate of interest offered by scheme A is approximately **19.9%**.