In a cricket game Dhoni is out for 52 runs which raises his average from 36 to 37. How many runs would he have to score in that innings (in which he scored 52) to raise his average to 39 ?

Options

A. 72
B. 84
C. 100
D. 82

Answer

To solve the problem step by step, we can follow these calculations:

1. **Understanding the Problem**: Dhoni's average increases from 36 to 37 after scoring 52 runs. We need to find out how many runs he would need to score in that innings to raise his average to 39.

2. **Setting Up the Initial Conditions**:
- Let \( N \) be the number of innings Dhoni played before scoring 52 runs.
- His total runs before scoring 52 runs can be expressed as \( 36N \) (since his average was 36).

3. **Calculating the New Average**:
- After scoring 52 runs, the total runs become \( 36N + 52 \).
- The total number of innings becomes \( N + 1 \).
- The new average is given as 37, so we can set up the equation:
\[ \frac{36N + 52}{N + 1} = 37 \]

4. **Cross Multiplying**:
- Cross-multiplying gives us:
\[ 36N + 52 = 37(N + 1) \]
- Expanding the right side:
\[ 36N + 52 = 37N + 37 \]

5. **Rearranging the Equation**:
- Rearranging the equation:
\[ 36N + 52 - 37N - 37 = 0 \]
- This simplifies to:
\[ -N + 15 = 0 \quad \Rightarrow \quad N = 15 \]

6. **Calculating Total Runs Before Scoring 52**:
- Now, substituting \( N \) back to find the total runs:
\[ \text{Total runs} = 36N = 36 \times 15 = 540 \]

7. **Finding Runs Needed for Average of 39**:
- Let \( X \) be the runs he would need to score to achieve an average of 39.
- The new total runs would then be \( 540 + X \) and the total innings would be \( N + 1 = 16 \).
- Setting up the equation for the new average:
\[ \frac{540 + X}{16} = 39 \]

8. **Cross Multiplying Again**:
- Cross-multiplying gives:
\[ 540 + X = 39 \times 16 \]
- Calculating \( 39 \times 16 = 624 \):
\[ 540 + X = 624 \]

9. **Solving for \( X \)**:
- Rearranging gives:
\[ X = 624 - 540 = 84 \]

Thus, Dhoni would have to score **84 runs** in that innings to raise his average to 39.