The following questions are accompanied by three statements A, B and C. You have to determine which statement(s) is/are necessary/sufficient to answer the question.
Rinku borrowed an amount of Rs.5000 each from Milan and Rahul. What is the rate of interest?
A. Rinku returned the amount of Rs 5400 after due date to Milan.
B. Rinku returned Rs.5900 to Rahul after due date.
C. Rinku returned the money to Milan by SI, whereas to Rahul by.compound interest

Options

A. Only A and B together are sufficient
B. Only B and C together are sufficient
C. A, B and C together are necessary
D. Either A and B together or B and C together are sufficient

Answer

To determine the rate of interest that Rinku paid on the borrowed amounts from Milan and Rahul, we will analyze the statements provided one by one.

### Step 1: Understand the Question
Rinku borrowed Rs. 5000 from both Milan and Rahul. We need to find out the rate of interest for these loans.

### Step 2: Analyze Statement A
Statement A states that Rinku returned Rs. 5400 to Milan after the due date.

- **Calculation**:
- Principal (P) = Rs. 5000
- Amount returned (A) = Rs. 5400
- Interest (I) = A - P = 5400 - 5000 = Rs. 400

Using the formula for Simple Interest (SI):
\[ SI = \frac{P \times R \times T}{100} \]

We can rearrange it to find the rate of interest (R):
\[ R = \frac{SI \times 100}{P \times T} \]

However, we do not know the time (T) for which the money was borrowed. Therefore, Statement A alone is not sufficient to determine the rate of interest.

### Step 3: Analyze Statement B
Statement B states that Rinku returned Rs. 5900 to Rahul after the due date.

- **Calculation**:
- Principal (P) = Rs. 5000
- Amount returned (A) = Rs. 5900
- Interest (I) = A - P = 5900 - 5000 = Rs. 900

Using the same formula for Simple Interest:
\[ R = \frac{SI \times 100}{P \times T} \]

Again, we do not know the time (T) for which the money was borrowed. Therefore, Statement B alone is also not sufficient to determine the rate of interest.

### Step 4: Analyze Statement C
Statement C states that Rinku returned the money to Milan by Simple Interest, whereas to Rahul by Compound Interest.

- This statement provides information about the type of interest applied but does not provide any numerical values or time period to calculate the rate of interest. Therefore, Statement C alone is not sufficient.

### Step 5: Combine Statements A and B
Now, let's combine Statements A and B.

From Statement A:
- Amount returned to Milan = Rs. 5400
- Interest paid to Milan = Rs. 400

From Statement B:
- Amount returned to Rahul = Rs. 5900
- Interest paid to Rahul = Rs. 900

We still do not know the time period for which the loans were taken, but we can derive two equations based on the two different types of interest (SI for Milan and CI for Rahul).

However, since we have two different amounts and two different types of interest, we can set up a system of equations to solve for the rate of interest if we assume the same time period for both loans.

### Conclusion
Combining both Statements A and B provides enough information to derive the rate of interest for both loans, assuming the same time period.

Thus, the answer is that Statements A and B together are sufficient to determine the rate of interest.

### Final Answer
**Statements A and B together are sufficient to answer the question.**

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