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 43 = 158 , 35 = 824 , 42 = 153 , then 32 = ?

Options

A. 84
B. 83
C. 85
D. 94

Explanation

To solve the problem, we need to identify the pattern or rule that relates the pairs of numbers given in the statements. Let's break it down step by step.

### Step 1: Analyze the first statement
The first statement is:
- \( 43 = 158 \)

To find the rule, let's break down the digits of 43:
- The first digit is 4 and the second digit is 3.

Now, we will square each digit and subtract 1:
- \( 4^2 - 1 = 16 - 1 = 15 \)
- \( 3^2 - 1 = 9 - 1 = 8 \)

Combining these results gives us:
- \( 15 \) and \( 8 \) which can be written as \( 158 \).

### Step 2: Analyze the second statement
The second statement is:
- \( 35 = 824 \)

Again, we break down the digits of 35:
- The first digit is 3 and the second digit is 5.

Now, we will square each digit and subtract 1:
- \( 3^2 - 1 = 9 - 1 = 8 \)
- \( 5^2 - 1 = 25 - 1 = 24 \)

Combining these results gives us:
- \( 8 \) and \( 24 \) which can be written as \( 824 \).

### Step 3: Analyze the third statement
The third statement is:
- \( 42 = 153 \)

Breaking down the digits of 42:
- The first digit is 4 and the second digit is 2.

Now, we will square each digit and subtract 1:
- \( 4^2 - 1 = 16 - 1 = 15 \)
- \( 2^2 - 1 = 4 - 1 = 3 \)

Combining these results gives us:
- \( 15 \) and \( 3 \) which can be written as \( 153 \).

### Step 4: Apply the rule to find the value of 32
Now, we need to find the value of:
- \( 32 = ? \)

Breaking down the digits of 32:
- The first digit is 3 and the second digit is 2.

Now, we will square each digit and subtract 1:
- \( 3^2 - 1 = 9 - 1 = 8 \)
- \( 2^2 - 1 = 4 - 1 = 3 \)

Combining these results gives us:
- \( 8 \) and \( 3 \) which can be written as \( 83 \).

### Final Answer
Thus, the value of \( 32 \) is \( 83 \).

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