To determine whether Mr. Gupta can repay the borrowed amount using the given statements, we will analyze each statement step by step.
### Step 1: Understand the question
The question asks for the total amount Mr. Gupta will repay after borrowing a sum of money on compound interest for 2 years.
### Step 2: Analyze Statement I
**Statement I: The rate of interest is 5% p.a.**
- We need to find the total amount to be repaid after 2 years. However, we do not know the principal amount borrowed. Without knowing the principal, we cannot calculate the total amount using the compound interest formula:
\[
A = P \left(1 + \frac{R}{100}\right)^N
\]
- Since we cannot determine the total amount with just this statement, we conclude that Statement I alone is insufficient.
### Step 3: Analyze Statement II
**Statement II: Simple interest fetched on the same amount in one year is Rs.600.**
- This statement gives us the simple interest for one year. We can use the formula for simple interest:
\[
SI = \frac{P \times R \times T}{100}
\]
- Here, \(SI = 600\), \(R = 5\%\), and \(T = 1\) year. We can rearrange the formula to find the principal:
\[
600 = \frac{P \times 5 \times 1}{100} \implies P = \frac{600 \times 100}{5} = 12000
\]
- Now that we have the principal amount \(P = 12000\), we can calculate the compound interest for 2 years using the rate from Statement I.
- However, this statement alone does not provide the necessary information about the time period for compound interest, so we cannot determine the total amount yet.
### Step 4: Analyze Statement III
**Statement III: The amount borrowed is 10 times the simple interest in 2 years.**
- From Statement II, we know the simple interest for 1 year is Rs.600. Therefore, the simple interest for 2 years is:
\[
SI_{2\text{ years}} = 600 \times 2 = 1200
\]
- According to Statement III, the amount borrowed is 10 times the simple interest for 2 years:
\[
Amount = 10 \times 1200 = 12000
\]
- This confirms the principal amount as Rs.12000.
### Step 5: Combine Statements
- With Statement II, we found the principal amount, and with Statement III, we confirmed it. Now, we can use the principal and the rate from Statement I to calculate the total amount to be repaid after 2 years.
- Using the compound interest formula:
\[
A = 12000 \left(1 + \frac{5}{100}\right)^2 = 12000 \left(1.05\right)^2 = 12000 \times 1.1025 = 13230
\]
- Therefore, the total amount to be repaid after 2 years is Rs.13230.
### Conclusion
To answer the question, we need Statements II and III. Statement I is not necessary because we already have the rate from Statement II. Thus, the answer is that we can dispense with Statement I.
### Final Answer
The answer number bearing the statements that can be dispensed with is **1**.
