Question

A batsman has a certain average of runs for 11 innings. In the 12\(^{\text{th}}\) inning. He makes a score of 90 runs, thereby increasing his average by 5. His new average is:

• A. 30
• B. 40
• C. 45
• D. 50
• E. 35

Hint:

Shortcut formula for the old average: \( \text{Old Average} = \text{New Score} - (\text{Total Innings} \times \text{Increase in Average}) = 90 - (12 \times 5) = 90 - 60 = 30 \). Therefore, the new average is \( 30 + 5 = 35 \).

Answer 1

Answer: (E)

Step 1: Understanding the Question:
The problem describes a scenario where a batsman's average score increases after playing an additional inning. We need to find his updated (new) average after the 12\(^{\text{th}}\) inning.


Step 2: Key Formula or Approach:
The fundamental mathematical formula for an average is:
\[ \text{Average} = \frac{\text{Sum of Observations}}{\text{Number of Observations}} \] We can set up a linear algebraic equation using the given relationship between the old average and the new average.


Step 3: Detailed Explanation:
Let the batsman's average for the first 11 innings be \( x \).
The total runs scored in the first 11 innings is \( 11x \).
In the 12\(^{\text{th}}\) inning, he scores exactly 90 runs.
So, the total sum of runs scored across all 12 innings becomes \( 11x + 90 \).
The problem states that the new average after 12 innings is \( x + 5 \).
Using the average formula for the 12 innings:
\[ \frac{11x + 90}{12} = x + 5 \] Multiply both sides of the equation by 12 to eliminate the denominator:
\[ 11x + 90 = 12(x + 5) \] \[ 11x + 90 = 12x + 60 \] Subtract \( 11x \) from both sides to isolate \( x \):
\[ 90 = x + 60 \] Subtract 60 from both sides:
\[ x = 30 \] So, the old average for the first 11 innings was 30.
Read the question carefully: It asks for his new average.
New average = \( x + 5 = 30 + 5 = 35 \).


Step 4: Final Answer:
The new average of the batsman is 35.