What is the rate of simple interest per annum ?
I. The sum triples in 20 years at simle interest.
II. The difference between the sum and the simple interest earned after 10 years is Rs. 1000.

Answer

To determine the rate of simple interest per annum, we will analyze the two statements provided.

### Step-by-Step Solution:

**Step 1: Analyze Statement I**
- The statement says that the sum triples in 20 years at simple interest.
- Let the principal amount be \( P \).
- The total amount after 20 years is \( 3P \).
- The formula for the total amount in simple interest is given by:
\[ \text{Total Amount} = \text{Principal} + \text{Simple Interest} \]
Thus, we can write:
\[ 3P = P + \text{Simple Interest} \]
- Rearranging gives:
\[ 3P - P = \text{Simple Interest} \implies 2P = \text{Simple Interest} \]
- The formula for simple interest is:
\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \]
where \( R \) is the rate of interest and \( T \) is the time in years.
- For \( T = 20 \) years, we have:
\[ 2P = \frac{P \times R \times 20}{100} \]
- Simplifying this:
\[ 2P = \frac{P \times R \times 20}{100} \implies 2 = \frac{R \times 20}{100} \]
- Multiplying both sides by 100:
\[ 200 = R \times 20 \]
- Dividing by 20:
\[ R = 10\% \]

**Conclusion from Statement I**: This statement is sufficient to determine the rate of simple interest.

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**Step 2: Analyze Statement II**
- The statement says that the difference between the sum and the simple interest earned after 10 years is Rs. 1000.
- The simple interest earned in 10 years is given by:
\[ \text{Simple Interest} = \frac{P \times R \times 10}{100} \]
- The total amount after 10 years is:
\[ \text{Total Amount} = P + \text{Simple Interest} = P + \frac{P \times R \times 10}{100} \]
- The difference between the total amount and the simple interest is:
\[ \left( P + \frac{P \times R \times 10}{100} \right) - \frac{P \times R \times 10}{100} = P \]
- According to the statement, this difference is Rs. 1000:
\[ P = 1000 \]
- However, this gives us the principal amount but does not provide any information about the rate of interest \( R \). We cannot determine \( R \) from this statement alone.

**Conclusion from Statement II**: This statement is not sufficient to determine the rate of simple interest.

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### Final Conclusion:
- Statement I is sufficient to determine the rate of simple interest.
- Statement II is not sufficient to determine the rate of simple interest.

Thus, the answer is that **only Statement I is sufficient**.