There is some average of 11 innings of a batsman. He scores 90 runs in `12^(th)` innings then average is decreased by 5 runs. Find his current average

Answer

To find the current average of the batsman after scoring 90 runs in the 12th inning, we can follow these steps:

### Step 1: Define the initial average
Let the average runs scored in the first 11 innings be \( x \).

### Step 2: Calculate the total runs after 11 innings
The total runs scored in the first 11 innings can be calculated as:
\[ \text{Total runs} = \text{Average} \times \text{Number of innings} = x \times 11 \]

### Step 3: Add the 12th inning score
After scoring 90 runs in the 12th inning, the new total runs becomes:
\[ \text{New total runs} = (x \times 11) + 90 \]

### Step 4: Calculate the new average
The new average after 12 innings is:
\[ \text{New average} = \frac{\text{New total runs}}{12} = \frac{(x \times 11) + 90}{12} \]

### Step 5: Set up the equation for the decrease in average
According to the problem, the new average is 5 runs less than the original average \( x \):
\[ \frac{(x \times 11) + 90}{12} = x - 5 \]

### Step 6: Clear the fraction by multiplying through by 12
Multiply both sides by 12 to eliminate the denominator:
\[ (x \times 11) + 90 = 12(x - 5) \]

### Step 7: Expand the right side
Expanding the right side gives:
\[ (x \times 11) + 90 = 12x - 60 \]

### Step 8: Rearrange the equation
Now, rearranging the equation to isolate \( x \):
\[ 11x + 90 + 60 = 12x \]
\[ 11x + 150 = 12x \]
\[ 150 = 12x - 11x \]
\[ 150 = x \]

### Step 9: Find the current average
Now that we have found \( x \) (the initial average), we can find the current average:
\[ \text{Current average} = x - 5 = 150 - 5 = 145 \]

### Final Answer
Thus, the current average of the batsman is **145**.

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