In the question , the length of the actual rope is given as 40 foot. Also it is given that the length of one rope after cutting the original piece of rope into 2 pieces is 9 times that of the other pice.
Let us assume that the length of one piece of rope is = X
Then the length of the orther pice of rope = 9X
Now we can easily get the equation
X + 9X = 40
10X = 40
X = 40/10
X = 4
So the length of the shorter rope is 4 foot.
The length of the longer rope is 9 times that of the shorter one.
So the length of the longer rope is 36 foot.