In each of the following questions , three statements of numbers following same rules are given . Find the rule and accordingly find the value of the number ?
If `3 + 2 = 7, 4 + 3 = 10, 5 + 4 =13 ,` then 6 + 5 = ?

Options

A. 17
B. 18
C. 15
D. 16

Explanation

To solve the problem, we need to identify the rule applied in the given statements and then use that rule to find the value of \(6 + 5\).

### Step 1: Analyze the given statements
The statements provided are:
1. \(3 + 2 = 7\)
2. \(4 + 3 = 10\)
3. \(5 + 4 = 13\)

### Step 2: Identify the pattern
Let's analyze the first statement:
- The first number is \(3\) and the second number is \(2\).
- If we keep the first number as it is and add twice the second number:
\[ 3 + (2 \times 2) = 3 + 4 = 7 \]
This matches the first statement.

Now, let's check the second statement:
- The first number is \(4\) and the second number is \(3\).
- Using the same rule:
\[ 4 + (2 \times 3) = 4 + 6 = 10 \]
This matches the second statement.

Now, let's check the third statement:
- The first number is \(5\) and the second number is \(4\).
- Again applying the same rule:
\[ 5 + (2 \times 4) = 5 + 8 = 13 \]
This matches the third statement as well.

### Step 3: Apply the rule to find \(6 + 5\)
Now that we have identified the rule, we can apply it to find \(6 + 5\):
- The first number is \(6\) and the second number is \(5\).
- Using the rule:
\[ 6 + (2 \times 5) = 6 + 10 = 16 \]

### Conclusion
Thus, \(6 + 5 = 16\).

### Final Answer
The value of \(6 + 5\) is \(16\).

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