The Problem:

We are given that a certain number, when increased by 20%, equals 42. We need to determine the original number.

Step 1: Understanding the Problem

To solve this problem, we first need to understand what it means to increase a number by 20%. When we increase a number by a certain percentage, we are adding that percentage of the original number to the original number.

In this case, we need to find a number x, such that when we increase it by 20%, we get 42.

Step 2: Setting up the Equation

Let's represent the original number as x. We can then set up the equation as follows:

x + 20% of x = 42

We know that 20% is equivalent to 0.2, so we can rewrite the equation as:

x + 0.2x = 42

Now, we can combine the terms on the left side of the equation:

1.2x = 42

Step 3: Solving for x

To isolate x, we can divide both sides of the equation by 1.2:

x = 42 / 1.2

Simplifying the right side of the equation gives us:

x = 35

Therefore, the original number is 35.

Step 4: Checking the Solution

To verify our answer, we can substitute the value of x back into the original equation:

35 + 20% of 35 = 35 + 0.2 * 35 = 35 + 7 = 42

Since the equation holds true, we can be confident that our solution is correct.

Conclusion:

The original number is 35.

35