Sanjay had a rope and he used a fraction of it to tie the boxes together. Afterwards, he used another fraction of the remaining rope to make a skipping rope for his daughter. Finally, he was left with 120 cm of rope. Let's break down the problem step by step to find out the original length of the rope.

Given Information:
- Sanjay used 1/4 of the rope to tie the boxes together.
- He used 5/9 of the remaining rope to make a skipping rope.
- Finally, 120 cm of rope was left.

Step 1: Finding the Length of the Rope Used to Tie the Boxes

To find the length of the rope used to tie the boxes, we need to calculate 1/4 of the original length of the rope.

Let's assume the original length of the rope is 'x' cm.

The length of the rope used to tie the boxes = (1/4) * x

Step 2: Finding the Remaining Length of the Rope

To find the remaining length of the rope after tying the boxes, we need to subtract the length used for tying the boxes from the original length of the rope.

Remaining length of the rope = x - (1/4) * x

Step 3: Finding the Length of the Skipping Rope

To find the length of the skipping rope made for Sanjay's daughter, we need to calculate 5/9 of the remaining length of the rope.

Length of the skipping rope = (5/9) * (x - (1/4) * x)

Step 4: Finding the Final Length of the Rope

The final length of the rope is the length of the skipping rope plus the length of the rope left after making the skipping rope.

Final length of the rope = Length of the skipping rope + Length of the remaining rope

Final length of the rope = (5/9) * (x - (1/4) * x) + 120

Step 5: Solving the Equation

We know that the final length of the rope is 120 cm, so we can set up the equation:

120 = (5/9) * (x - (1/4) * x) + 120

Simplifying the equation:

0 = (5/9) * (x - (1/4) * x)

0 = (5/9) * (3/4) * x

0 = (15/36) * x

x = 0

Conclusion:

The original length of the rope is 0 cm. This means that there was no rope to begin with, or there was an error in the given information.