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.

Step-by-step derivation:

1. Find the initial sum of the 10 numbers:
The average of 10 numbers is given as 30.
$\text{Original Sum}=\text{Average}\times \text{Total numbers}$
$\text{Original Sum}=30\times 10=300$

2. Find the new sum after replacement:
When one of the numbers is replaced by 50, the average increases by 2. Thus, the new average becomes:
$30+2=32$
The new sum of the 10 numbers is:
$\text{New Sum}=32\times 10=320$

3. Calculate the difference between the sums:
The difference between the new sum and the original sum is due to replacing the old number with 50.
$\text{Increase in sum}=\text{New Sum}-\text{Original Sum}$
$\text{Increase in sum}=320-300=20$

4. Find the replaced number:
Let the replaced number be $x$.
Since replacing $x$ with 50 increased the overall sum by 20, we set up the following equation:
$50-x=20$
Solving for $x$:
$x=50-20$
$x=30$

Therefore, the number that was replaced is 30.