A man on a rung of ladder notices there are twice as many rungs below him than above him he descends eight rungs he notices that the no of rungs below above him are equal how many rungs on ladder?

Answer 1

Okay so to start out, we need to form an equation to simulate this problem. I'm going to use x as the number of rungs below the man the first time he looks, and y as the number of rungs above the man the first time he looks. My initial equation is the following.

2y=x or y=(x/2) and x+y=z

Since there are twice as many rungs below him (x) as there are above him, you'd need to divide x by two in order to get it equal to the amount above him. Hence the y=(x/2) equation. This equation can also be written as 2y=x. Also, I'm using z as the total number of rungs on the ladder.

The second part of the problem states that the man moves down the ladder 8 rungs which leads to equal rungs on both sides. If he moves down the ladder 8 rungs, it means that the amount below him decreases by 8 (so x-8) and the number of rungs above him increase by 8 (so y+8). Since they end up equal, you can write the equation (x-8=y+8) which can also be written as (y=x-16) or (x=y+16).

x-8=y+8 or y=x-16 or x=y+16

Now that we have two equations, we can solve for a variable using substitution. Please note that you can substitute in for x or y, depending on which you feel like doing.

2(x-16)=x

Here I substituted x-16 in for y (2y=x). You could easily substitute y+16 in for x.

2x-32=x

Multiplied out and got rid of the parenthesis.

x=32

Isolated x.

Now that we know x (the original amount of rungs below him) is equal to 32, we need to solve for y in order to find out the total number of rungs.

y=x/2

Using the equation from before.

y=(32/2)
y=16

Plugging 32 in for x and solving.

You can double check this by comparing it to the question. If the man starts out with 32 rungs below him and 16 above him, then does he have twice as many rungs below him than above him? (yes). Now if you subtract 8 rungs from below him (32-8=24) and add 8 rungs above him (16+8=24) do they end up the same? (24=24, yes). Now that we are sure that these two values are correct, we continue to the next step.

We take x=32 (number of rungs originally below the man) and y=16 (number of rungs originally above the man) and add them to find the total number of rungs (x+y=z). 32+16=z
z=48.
z is the total number of rungs on the ladder, and since z=48 then we know that there are 48 rungs on the ladder.