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 xx 4 = 14, 5 xx 6 = 33, 7 xx 8 = 60` , then `8 xx 9 = ?`

Options

A. 77
B. 89
C. 98
D. 79

Explanation

To solve the problem step by step, we need to identify the pattern in the given statements.

### Step 1: Analyze the given equations
We have three equations:
1. \(3 \times 4 = 14\)
2. \(5 \times 6 = 33\)
3. \(7 \times 8 = 60\)

### Step 2: Calculate the products
Let's calculate the products of the pairs:
- For \(3 \times 4\):
\[ 3 \times 4 = 12 \]
- For \(5 \times 6\):
\[ 5 \times 6 = 30 \]
- For \(7 \times 8\):
\[ 7 \times 8 = 56 \]

### Step 3: Find the difference between the product and the given result
Now, let's find out how much we need to add to each product to get the result:
- For \(3 \times 4\):
\[ 12 + 2 = 14 \quad (\text{added } 2) \]
- For \(5 \times 6\):
\[ 30 + 3 = 33 \quad (\text{added } 3) \]
- For \(7 \times 8\):
\[ 56 + 4 = 60 \quad (\text{added } 4) \]

### Step 4: Identify the pattern
From the calculations, we can see that:
- We added \(2\) to the product of \(3 \times 4\)
- We added \(3\) to the product of \(5 \times 6\)
- We added \(4\) to the product of \(7 \times 8\)

The pattern shows that we are adding consecutive integers starting from \(2\).

### Step 5: Apply the pattern to \(8 \times 9\)
Now, we need to find \(8 \times 9\):
- Calculate the product:
\[ 8 \times 9 = 72 \]
- According to the pattern, we should add \(5\) (the next consecutive integer after \(4\)):
\[ 72 + 5 = 77 \]

### Conclusion
Thus, the value of \(8 \times 9\) according to the established rule is:
\[ \boxed{77} \]