The average of 10 numbers is 30. When one number is replaced by 50, the average increases by 2. Find the number that was replaced.

The correct option is 30.

Let's break down the solution step-by-step:

Step 1: Find the initial sum of the 10 numbers.
The average of 10 numbers is given as 30. Using the formula for the average:
$\text{Average}=\frac{\text{Sum of numbers}}{\text{Total count of numbers}}$
Therefore, the initial sum of the 10 numbers is:
$\text{Initial Sum}=10\times 30=300$

Step 2: Understand the effect of the replacement.
Let the number that was replaced be represented by:
$x$
When this number is removed and replaced by 50, the new sum becomes:
$\text{New Sum}=300-x+50=350-x$

Step 3: Determine the new sum using the new average.
We are told that the average increases by 2. Thus, the new average is:
$30+2=32$
Since the total count of numbers remains 10, the new sum is:
$\text{New Sum}=10\times 32=320$

Step 4: Solve for the replaced number.
Now, equate the two expressions for the new sum:
$350-x=320$
Solving for the replaced number:
$x=350-320$
$x=30$

Thus, the number that was replaced is 30.