Statement-1: the sum of the diigits in the ten's place of all numbers formed with the help of 3,4,5,6 taken all at a time is 108.
Statement-2: The sum of the digits in the ten's place= The sum of the digits is the units's place.

Options

A. Statement-1 is true, statement-2 is true, statement-2 is a correct explanation for statement-1
B. Statement-1 is true, statement-2 is true, statement-2 is not a correct explanation for statement-1
C. Statement-1 is true, statement-2 is false
D. Statement-1 is false, statement-2 is true

Explanation

To solve the problem, we need to analyze both statements provided in the question.

### Step 1: Understanding the Problem
We are given four digits: 3, 4, 5, and 6. We need to form all possible numbers using these digits and then analyze the sum of the digits in the tens place.

### Step 2: Calculate the Total Numbers Formed
Since we have 4 distinct digits and we are using all of them at a time, the total number of permutations of these digits is given by:
\[ 4! = 24 \]
This means we can form 24 different numbers using the digits 3, 4, 5, and 6.

### Step 3: Identify the Tens Place Contribution
In each of these 24 numbers, we need to determine how many times each digit appears in the tens place.

1. **Fixing the Tens Place**:
- If we fix a digit in the tens place, we can arrange the remaining 3 digits in the other places (units, hundreds, thousands).
- The number of arrangements of the remaining 3 digits is \(3! = 6\).

2. **Counting Contributions**:
- Each digit (3, 4, 5, 6) will appear in the tens place for 6 different numbers.
- Therefore, the contribution of each digit to the tens place can be calculated as follows:
- Contribution of 3 in tens place: \(3 \times 6 = 18\)
- Contribution of 4 in tens place: \(4 \times 6 = 24\)
- Contribution of 5 in tens place: \(5 \times 6 = 30\)
- Contribution of 6 in tens place: \(6 \times 6 = 36\)

### Step 4: Summing the Contributions
Now, we sum all the contributions from the tens place:
\[ 18 + 24 + 30 + 36 = 108 \]
Thus, the sum of the digits in the tens place of all numbers formed is indeed 108.

### Step 5: Analyzing Statement 2
The second statement claims that the sum of the digits in the tens place equals the sum of the digits in the units place.

- By similar reasoning, since the arrangement of digits is symmetric, each digit will also appear in the units place the same number of times as in the tens place. Therefore, the sum of the digits in the units place will also be:
\[ 18 + 24 + 30 + 36 = 108 \]
This confirms that the second statement is true.

### Conclusion
Both statements are true, and the second statement is a correct explanation of the first statement.

### Final Answer
- Statement 1 is true.
- Statement 2 is true and explains Statement 1.

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