A cricketer's average score over a series of matches is 42. If she scores 138 runs in the next match, her average increases to 46. How many matches did she play before this?

The correct option is 23.

Step-by-Step Explanation:

Step 1: Define the variables

Let $n$ be the number of matches the cricketer played before the last match.

The original average score over these $n$ matches is 42 runs.

Step 2: Calculate the total runs before the last match

The formula for the average score is:

$\text{Average}=\frac{\text{Total Runs}}{\text{Number of Matches}}$

Therefore, the total runs scored in the first $n$ matches is:

$\text{Total Runs}=42\times n=42n$

Step 3: Set up the equation for the new average

In the next match, she scores 138 runs.

The new total number of matches played becomes $n+1$.

The new total runs scored across all matches is $42n+138$.

We are given that the new average increases to 46. So, we can write the equation:

$\frac{42n+138}{n+1}$

Step 4: Solve for $n$

Multiply both sides of the equation by $(n+1)$:

$42n+138=46(n+1)$

Expand the right side:

$42n+138=46n+46$

Subtract $42n$ from both sides:

$138=4n+46$

Subtract 46 from both sides:

$138-46=4n$

$92=4n$

Divide by 4:

$n=\frac{92}{4}$

$n=23$

Thus, the number of matches she played before this match is 23.