A cricket player after playing 10 tests scored 100 runs in the 11th test. As a result, the average of his runs is increased by 5. The present average of runs is

Options

A. 45
B. 40
C. 50
D. 55

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the variables
Let the average runs scored by the cricket player after 10 tests be \( x \).

### Step 2: Calculate the total runs after 10 tests
The total runs scored after 10 tests can be expressed as:
\[ \text{Total runs after 10 tests} = 10x \]

### Step 3: Add the runs scored in the 11th test
The player scored 100 runs in the 11th test. Therefore, the total runs after 11 tests becomes:
\[ \text{Total runs after 11 tests} = 10x + 100 \]

### Step 4: Calculate the new average
The new average after 11 tests is given by:
\[ \text{New average} = \frac{\text{Total runs after 11 tests}}{11} = \frac{10x + 100}{11} \]

### Step 5: Set up the equation for the increase in average
According to the problem, the new average is 5 runs more than the previous average:
\[ \frac{10x + 100}{11} = x + 5 \]

### Step 6: Solve the equation
To eliminate the fraction, multiply both sides by 11:
\[ 10x + 100 = 11(x + 5) \]
Expanding the right side:
\[ 10x + 100 = 11x + 55 \]
Rearranging the equation gives:
\[ 100 - 55 = 11x - 10x \]
\[ 45 = x \]

### Step 7: Find the present average
The present average after 11 tests is:
\[ \text{Present average} = x + 5 = 45 + 5 = 50 \]

### Final Answer
Thus, the present average of runs is **50**.

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