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 + 9 = 31 , 15 +12 = 45 , 18 + 9 = 36 ` then 12 + 27 = ?

Options

A. 94
B. 14
C. 49
D. 53

Explanation

To solve the problem step by step, we need to identify the rule applied in the given statements and then apply that same rule to find the value of \( 12 + 27 \).

### Step 1: Analyze the given statements
We have three statements:
1. \( 3 + 9 = 31 \)
2. \( 15 + 12 = 45 \)
3. \( 18 + 9 = 36 \)

### Step 2: Identify the pattern
Let's analyze the first statement:
- \( 3 + 9 = 12 \) (normal addition)
- The result given is \( 31 \).

Now, let's see if there is a way to manipulate \( 12 \) to get \( 31 \):
- If we divide \( 3 \) by \( 3 \), we get \( 1 \).
- If we divide \( 9 \) by \( 3 \), we get \( 3 \).
- Combining these gives us \( 13 \) (not \( 31 \)).

Now let's try reversing the digits:
- If we take \( 12 \) and reverse it, we get \( 21 \) (not \( 31 \)).

Let's try another approach:
- If we divide \( 3 \) by \( 3 \) and \( 9 \) by \( 3 \):
- \( 3 / 3 = 1 \)
- \( 9 / 3 = 3 \)
- Combine them: \( 13 \) (not \( 31 \)).

### Step 3: Check the second statement
Now, let's analyze the second statement:
- \( 15 + 12 = 27 \) (normal addition)
- The result given is \( 45 \).
- Dividing:
- \( 15 / 3 = 5 \)
- \( 12 / 3 = 4 \)
- Combine them: \( 54 \).
- If we reverse \( 54 \), we get \( 45 \) (which matches).

### Step 4: Check the third statement
Now, let's analyze the third statement:
- \( 18 + 9 = 27 \) (normal addition)
- The result given is \( 36 \).
- Dividing:
- \( 18 / 3 = 6 \)
- \( 9 / 3 = 3 \)
- Combine them: \( 63 \).
- If we reverse \( 63 \), we get \( 36 \) (which matches).

### Step 5: Establish the rule
From the above analysis, we can conclude that the rule is:
1. Divide both numbers by \( 3 \).
2. Combine the results.
3. Reverse the digits of the combined result to get the final answer.

### Step 6: Apply the rule to \( 12 + 27 \)
Now, let's apply the same rule to \( 12 + 27 \):
1. Divide \( 12 \) by \( 3 \):
\[ 12 / 3 = 4 \]
2. Divide \( 27 \) by \( 3 \):
\[ 27 / 3 = 9 \]
3. Combine the results:
\[ 4 \text{ and } 9 \text{ gives us } 49. \]
4. Reverse \( 49 \):
\[ \text{Reversed } 49 \text{ is } 94. \]

### Final Answer
Thus, \( 12 + 27 = 94 \).

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