Apologies for the delayed posting of the solution – I was on vacation on both of the previous weekends, traveling outside the country.
As I mentioned in the puzzle, this was a lateral thinking puzzle. The first person to answer this puzzle was Ruchir Godura – who answered this within a few minutes probably!
Here is the solution – Rajeev uses the knife to cut the rope at 50M length. He make a loop at one end and ties the other one to the hook. Through this loop, he takes the remaining 100M rope and then ties both the end of the 100M rope. This way he has a rope of 100M (50M shorter one, and a double rope of 50M hanging through the loop of the smaller one) to come down to the ledge. One he reaches the ledge, he can pull the longer rope until he finds the knot, unties it, and now he has a 100M rope with which he can come down. Answer is also explained in the video on this link:
Hope you enjoyed this.