The average score of Dhoni after 48 innings is 48 and in the 49th innings Dhoni scores 97 runs.In the 50th innings the minimum number of runs required to increase his average score by 2 than it was before the 50th innings:

Options

A. 99
B. 149
C. 151
D. can't be determined

Answer

To solve the problem, we need to follow these steps:

### Step 1: Calculate the total score after 48 innings
The average score after 48 innings is given as 48. To find the total score after these innings, we can use the formula:

\[ \text{Total Score} = \text{Average} \times \text{Number of Innings} \]

Substituting the values:

\[ \text{Total Score after 48 innings} = 48 \times 48 = 2304 \]

### Step 2: Add the score from the 49th inning
In the 49th inning, Dhoni scores 97 runs. We need to add this score to the total score from the previous innings:

\[ \text{Total Score after 49 innings} = 2304 + 97 = 2401 \]

### Step 3: Calculate the average after 49 innings
Now, we can find the average score after 49 innings:

\[ \text{Average after 49 innings} = \frac{\text{Total Score after 49 innings}}{\text{Number of Innings}} \]

Substituting the values:

\[ \text{Average after 49 innings} = \frac{2401}{49} = 49 \]

### Step 4: Determine the new average after the 50th inning
We want to increase the average by 2 runs, so the new average after the 50th inning should be:

\[ \text{New Average} = 49 + 2 = 51 \]

### Step 5: Calculate the total score required for the new average
To find the total score required to achieve this new average after 50 innings, we use the formula again:

\[ \text{Total Score required for new average} = \text{New Average} \times \text{Number of Innings} \]

Substituting the values:

\[ \text{Total Score required for new average} = 51 \times 50 = 2550 \]

### Step 6: Calculate the runs needed in the 50th inning
Now, we can find out how many runs Dhoni needs to score in the 50th inning to reach this total score:

\[ \text{Runs required in 50th inning} = \text{Total Score required for new average} - \text{Total Score after 49 innings} \]

Substituting the values:

\[ \text{Runs required in 50th inning} = 2550 - 2401 = 149 \]

### Final Answer
The minimum number of runs required in the 50th inning to increase Dhoni's average score by 2 is **149 runs**.

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