What is the rate of interest at which Binod has invested money?
A. The compound interest at this rate of Rs.2500 in 2 yrs is equal to the simple interest in 3 yrs of Rs. 5150 at the same rate.
B. The total simple interest on an investment of Rs. 12000 for 3 yrs and Rs. 10000 for 5 yrs at this rate is R. 5160
C. In 3 yrs Rs. 1500 at the same rate becomes Rs. 1725 by simple interest.

Options

A. Any of them
B. A and either B or C
C. Only C
D. Only A and either B or C

Explanation

To find the rate of interest at which Binod has invested money, we will analyze each statement (A, B, and C) provided in the question step by step.

### Step 1: Analyze Statement A
**Statement A:** The compound interest at this rate of Rs. 2500 in 2 years is equal to the simple interest in 3 years of Rs. 5150 at the same rate.

1. **Compound Interest Formula:**
\[ A = P(1 + \frac{R}{100})^T \]
where \( A \) is the amount after time \( T \), \( P \) is the principal, \( R \) is the rate of interest, and \( T \) is the time in years.

For \( P = 2500 \) and \( T = 2 \):
\[ A = 2500(1 + \frac{R}{100})^2 \]
The compound interest (CI) will be:
\[ CI = A - P = 2500(1 + \frac{R}{100})^2 - 2500 \]

2. **Simple Interest Formula:**
\[ SI = \frac{P \times R \times T}{100} \]
For \( P = 5150 \) and \( T = 3 \):
\[ SI = \frac{5150 \times R \times 3}{100} \]

3. **Setting the two interests equal:**
\[ 2500(1 + \frac{R}{100})^2 - 2500 = \frac{5150 \times R \times 3}{100} \]

This gives us one equation with one unknown \( R \).

### Step 2: Analyze Statement B
**Statement B:** The total simple interest on an investment of Rs. 12000 for 3 years and Rs. 10000 for 5 years at this rate is Rs. 5160.

1. **Calculate Simple Interest for both investments:**
- For Rs. 12000 for 3 years:
\[ SI_1 = \frac{12000 \times R \times 3}{100} \]
- For Rs. 10000 for 5 years:
\[ SI_2 = \frac{10000 \times R \times 5}{100} \]

2. **Setting the total simple interest equal to Rs. 5160:**
\[ SI_1 + SI_2 = 5160 \]
\[ \frac{12000 \times R \times 3}{100} + \frac{10000 \times R \times 5}{100} = 5160 \]

This also gives us one equation with one unknown \( R \).

### Step 3: Analyze Statement C
**Statement C:** In 3 years, Rs. 1500 at the same rate becomes Rs. 1725 by simple interest.

1. **Calculate the Simple Interest:**
\[ SI = A - P = 1725 - 1500 = 225 \]
Using the simple interest formula:
\[ 225 = \frac{1500 \times R \times 3}{100} \]

2. **Rearranging to find \( R \):**
\[ R = \frac{225 \times 100}{1500 \times 3} \]

This gives us a direct calculation for \( R \).

### Conclusion
From the analysis of each statement:
- **Statement A** provides an equation to find \( R \).
- **Statement B** also provides an equation to find \( R \).
- **Statement C** directly allows us to calculate \( R \).

Thus, any of the statements A, B, or C is sufficient to determine the rate of interest.

### Final Answer
The answer is that any of the statements A, B, or C is sufficient to find the rate of interest.

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