The average runs scored by a batsman in forty-five matches were 42 runs. The difference between his highest and lowest runs scored was 114. If those two matches (in which he- scored the highest and the lowest runs) are excluded, his average score will be 40. What will be his lowest score ?

Options

A. 25
B. 32
C. 34
D. 28

Answer

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

### Step 1: Calculate the total runs scored in 45 matches.
The average runs scored by the batsman in 45 matches is 42 runs.

Total runs scored = Average runs × Number of matches
Total runs scored = 42 × 45 = 1890 runs

### Step 2: Define the lowest and highest scores.
Let the lowest score be \( X \).
According to the problem, the highest score will be \( X + 114 \) (since the difference between the highest and lowest scores is 114).

### Step 3: Calculate the total runs scored in the remaining 43 matches.
When the highest and lowest scores are excluded, the average score of the remaining matches is given as 40.

Total runs scored in 43 matches = Average runs × Number of matches
Total runs scored in 43 matches = 40 × 43 = 1720 runs

### Step 4: Set up the equation.
The total runs scored in 45 matches is the sum of the runs scored in the 43 matches plus the highest and lowest scores:

Total runs = Runs in 43 matches + Highest score + Lowest score
1890 = 1720 + (X + 114) + X

### Step 5: Simplify the equation.
1890 = 1720 + 2X + 114
1890 = 1834 + 2X
1890 - 1834 = 2X
56 = 2X
X = 28

### Step 6: Find the lowest score.
The lowest score is \( X \), which we found to be 28.

### Final Answer:
The lowest score is **28**.