The average runs scored by a cricketer in 42 innings, is 30. The difference between his maximum and minimum scores in an innings is 100. if these two innings are not taken into consideration , then the average score of remaining 40 innings is 28. calculate the maximum runs scored by hin in an innings ?

Options

A. 125
B. 120
C. 110
D. 100

Answer

To solve the problem step by step, we will use the information provided in the question:

1. **Calculate the total runs scored in 42 innings:**
- Given that the average runs scored in 42 innings is 30, we can calculate the total runs.
- Total runs = Average × Number of innings = 30 × 42 = 1260.

2. **Calculate the total runs scored in the remaining 40 innings:**
- The average score of the remaining 40 innings is 28.
- Total runs in 40 innings = Average × Number of innings = 28 × 40 = 1120.

3. **Determine the total runs scored in the two innings (maximum and minimum):**
- The total runs scored in the two innings (maximum and minimum) can be found by subtracting the total runs of the remaining 40 innings from the total runs of all 42 innings.
- Total runs in two innings = Total runs in 42 innings - Total runs in 40 innings = 1260 - 1120 = 140.

4. **Set up the equation for maximum and minimum scores:**
- Let the minimum score be \( x \) and the maximum score be \( x + 100 \) (since the difference between the maximum and minimum scores is 100).
- Therefore, we can write the equation:
\[ x + (x + 100) = 140. \]
- Simplifying this gives:
\[ 2x + 100 = 140. \]

5. **Solve for the minimum score \( x \):**
- Rearranging the equation:
\[ 2x = 140 - 100, \]
\[ 2x = 40, \]
\[ x = 20. \]
- Thus, the minimum score is 20.

6. **Calculate the maximum score:**
- The maximum score can now be calculated as:
\[ \text{Maximum score} = x + 100 = 20 + 100 = 120. \]

**Final Answer:**
The maximum runs scored by him in an innings is **120**.

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