Steve the builder was plastering a wall while standing on a ladder..he noticed that the number of rungs/steps below,the rung he was standing on was 1/3 of the numbers of rungs above where he was standing.

Then he climed another 10 rungs/steps and he also notice that the number of rungs below and above where he was standing are now equal....how many rungs are on the ladder

If the number below was x, then

x + 3x = 2(x+10)
x = 10

check:
10+30 = 20+20

Let's break down the problem and find a solution.

Let's represent the total number of rungs on the ladder as 'x'.

According to the problem, Steve noticed that the number of rungs below the rung he was standing on was one-third of the number of rungs above where he was standing. We can set up the following equation:

Number of rungs below = (1/3) * Number of rungs above

Since Steve was standing on a rung, the number of rungs below him is (x - 1). And the number of rungs above him is (x - (x - 1)) = 1. We can rewrite the equation as:

(x - 1) = (1/3) * 1

Simplifying the equation, we get:

x - 1 = 1/3

To get rid of the fraction, we can multiply both sides by 3:

3 * (x - 1) = 3 * (1/3)

3x - 3 = 1

Adding 3 to both sides of the equation:

3x - 3 + 3 = 1 + 3

3x = 4

Dividing both sides by 3, we get:

x = 4/3

But since we are dealing with rungs, x cannot be a fraction. We need to find a whole number solution.

Now, let's consider the second observation Steve made after climbing another 10 rungs. He noticed that the number of rungs below him and the number of rungs above him were equal.

Number of rungs below (after climbing 10 rungs) = Number of rungs above (after climbing 10 rungs)

(x - 1) + 10 = (x - 11)

Simplifying the equation:

x - 1 + 10 = x - 11

x + 9 = x - 11

Subtracting x from both sides:

9 = -11

This is not a true statement, which means there is no valid solution for x.

Therefore, based on the given information, there is no conclusive solution for the number of rungs on the ladder.