Question

"A firefighter stood on the middle rung of a ladder. When the smoke became less thick, the firefighter moved up 4 rungs. Then it got too hot, and the firefighter moved down 6 rungs. Later, the firefighter went up 7 rungs and stayed there till the fire was out. After the fire was out, the firefighter climbed the remaining 4 rungs and entered the building. How many rungs does the ladder have?"

Answer 1

There are 18 rungs on the ladder.

Explanation:

Given a firefighter who is standing on the middle of the ladder.

We have to find the number of rungs the ladder have.

Let the number of rungs be "2x" where "x" be the number of rungs from the middle of the ladder to the top of the ladder.

Rungs below the middle of the ladder is equal to rungs above the middle of the ladder.

According to the question:

Let the fire fighter be at "y" rungs this "y" will be the reference point.

⇒ Moved
`4` rungs from 'y' current position
`4` rungs above of 'y'.

⇒ Moved
`6` rungs down meaning that
`(4-6)= -2` rung from 'y' below
`2` rung downward from 'y'.

⇒ Moved
`7` rungs upward from here meaning
`(-2+7) = 5` rung above 'y'.

Now,

⇒ Further the firefighter climbed
`4` rungs from here
`(5+4) = 9` rungs above 'y' .

Finally the firefighter have climbed
`9` rungs from 'y' that is the middle of the ladder so there is equal rungs below of it.

Total rungs of the ladder = '2x' = 2(9) = 18 rungs.