A batsmen's average before the last two innings of a seasons was 66. He failed to score in those innnings and his average dropped to 55. How many innings did he play that season.

Options

A. 10
B. 11
C. 12
D. 8

Answer

To solve the problem, we need to find how many innings the batsman played that season based on the information given about his average scores.

Let's break it down step by step:

1. **Understand the Given Information:**
- The batsman's average before the last two innings was 66.
- He played a total of \( X \) innings before the last two innings.
- He scored 0 in the last two innings.
- After these two innings, his average dropped to 55.

2. **Calculate Total Runs Before Last Two Innings:**
- The total runs scored by the batsman before the last two innings can be calculated as:
\[ \text{Total Runs} = \text{Average} \times \text{Number of Innings} = 66 \times (X - 2) \]

3. **Calculate Total Runs After Last Two Innings:**
- After the last two innings where he scored 0, the total number of innings becomes \( X \).
- The new average is 55, so the total runs after all innings can be expressed as:
\[ \text{Total Runs After Last Two Innings} = 55 \times X \]

4. **Set Up the Equation:**
- Since the total runs before the last two innings plus the runs scored in the last two innings must equal the total runs after all innings, we can set up the equation:
\[ 66(X - 2) + 0 + 0 = 55X \]

5. **Simplify the Equation:**
- Expanding the left side:
\[ 66X - 132 = 55X \]

6. **Rearranging the Equation:**
- Move \( 55X \) to the left side:
\[ 66X - 55X = 132 \]
- This simplifies to:
\[ 11X = 132 \]

7. **Solve for \( X \):**
- Divide both sides by 11:
\[ X = \frac{132}{11} = 12 \]

8. **Conclusion:**
- Therefore, the total number of innings played by the batsman that season is **12**.