A cricket batsman had certain average of runs in his 91 innings. In the 92th inning, he made a score of 54 runs and thereby his average of runs was decreased by 0.75. His average of runs after 92th innings is :

Options

A. 122.25
B. 123.75
C. 123
D. 121.5

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define Variables
Let the average runs scored by the batsman in the first 91 innings be \( X \).

### Step 2: Calculate Total Runs for 91 Innings
The total runs scored in 91 innings can be expressed as:
\[ \text{Total Runs in 91 Innings} = 91X \]

### Step 3: Calculate Total Runs After 92 Innings
In the 92nd inning, the batsman scored 54 runs. Therefore, the total runs after 92 innings becomes:
\[ \text{Total Runs in 92 Innings} = 91X + 54 \]

### Step 4: Calculate New Average After 92 Innings
The average runs after 92 innings is given by:
\[ \text{New Average} = \frac{91X + 54}{92} \]

### Step 5: Set Up the Equation for Average Decrease
According to the problem, the new average is 0.75 less than the previous average:
\[ \frac{91X + 54}{92} = X - 0.75 \]

### Step 6: Clear the Fraction
To eliminate the fraction, multiply both sides by 92:
\[ 91X + 54 = 92(X - 0.75) \]

### Step 7: Distribute on the Right Side
Distributing the right side gives:
\[ 91X + 54 = 92X - 69 \]

### Step 8: Rearrange the Equation
Rearranging the equation to isolate \( X \):
\[ 54 + 69 = 92X - 91X \]
\[ 123 = X \]

### Step 9: Calculate the New Average
Now that we have \( X \), we can find the new average:
\[ \text{New Average} = X - 0.75 = 123 - 0.75 = 122.25 \]

### Final Answer
The average of runs after the 92nd innings is:
\[ \text{Average after 92 innings} = 122.25 \]

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