A batsman scores 556 run in 26th, 27th, 28th and 29th innings together and now his average increases by 4 runs. Find average run after 29th match.

Options

A. 107
B. 110
C. 114
D. 106

Answer

To solve the problem step by step, we will find the average runs scored by the batsman after his 29th match.

### Step 1: Define the variables
Let the runs scored in the 25th match be \( X \).

### Step 2: Calculate the average after 25 matches
The total runs scored after 25 matches is \( X \). Therefore, the average after 25 matches is:
\[ \text{Average}_{25} = \frac{X}{25} \]

### Step 3: Calculate total runs after 29 matches
The batsman scores a total of 556 runs in the 26th, 27th, 28th, and 29th innings. Therefore, the total runs scored after 29 matches is:
\[ \text{Total runs}_{29} = X + 556 \]

### Step 4: Calculate the new average after 29 matches
The average after 29 matches is given by:
\[ \text{Average}_{29} = \frac{X + 556}{29} \]

### Step 5: Set up the equation for the increase in average
According to the problem, the average increases by 4 runs. Therefore, we can express the new average as:
\[ \text{Average}_{29} = \text{Average}_{25} + 4 \]
Substituting the values we have:
\[ \frac{X + 556}{29} = \frac{X}{25} + 4 \]

### Step 6: Clear the fractions by cross-multiplying
Cross-multiplying gives:
\[ 25(X + 556) = 29X + 2900 \]

### Step 7: Expand and simplify the equation
Expanding the left side:
\[ 25X + 13900 = 29X + 2900 \]
Rearranging gives:
\[ 13900 - 2900 = 29X - 25X \]
\[ 11000 = 4X \]

### Step 8: Solve for \( X \)
Dividing both sides by 4:
\[ X = \frac{11000}{4} = 2750 \]

### Step 9: Calculate the new average after 29 matches
Now substituting \( X \) back into the average formula:
\[ \text{Average}_{29} = \frac{2750 + 556}{29} \]
Calculating the total:
\[ \text{Average}_{29} = \frac{3306}{29} \]

### Step 10: Perform the division
Calculating \( 3306 \div 29 \):
\[ \text{Average}_{29} = 114 \]

Thus, the average runs after the 29th match is **114**.

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