A cricketer scored some runs in his continuous 19 innings. He scored 100 runs in his 20th innings and this increased his average by 4 runs. What was the average of his runs at the end of 20th innings?

Options

A. 20
B. 24
C. 28
D. 32

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the average of the first 19 innings
Let the average runs scored in the first 19 innings be \( x \).

### Step 2: Calculate the total runs scored in the first 19 innings
The total runs scored in the first 19 innings can be calculated as:
\[ \text{Total runs in 19 innings} = 19 \times x \]

### Step 3: Add the runs scored in the 20th innings
In the 20th innings, the cricketer scored 100 runs. Therefore, the total runs after 20 innings will be:
\[ \text{Total runs after 20 innings} = 19x + 100 \]

### Step 4: Determine the new average after 20 innings
The new average after 20 innings will be:
\[ \text{New average} = \frac{19x + 100}{20} \]

### Step 5: Set up the equation for the increase in average
According to the problem, this new average is 4 runs more than the previous average \( x \):
\[ \frac{19x + 100}{20} = x + 4 \]

### Step 6: Clear the fraction by multiplying both sides by 20
To eliminate the fraction, multiply both sides by 20:
\[ 19x + 100 = 20(x + 4) \]

### Step 7: Expand the right side
Expanding the right side gives:
\[ 19x + 100 = 20x + 80 \]

### Step 8: Rearrange the equation to isolate \( x \)
Now, rearranging the equation to solve for \( x \):
\[ 19x + 100 - 80 = 20x \]
\[ 19x + 20 = 20x \]
\[ 20 = 20x - 19x \]
\[ 20 = x \]

### Step 9: Calculate the new average
Now that we have \( x = 20 \), we can find the new average:
\[ \text{New average} = x + 4 = 20 + 4 = 24 \]

### Conclusion
Thus, the average of the cricketer's runs at the end of the 20th innings is **24**.