For those who haven't read the puzzle, first give it a try at Burning Rope Timer Puzzle

Keep both the ropes alongside. As it is said the ropes are not uniform and both burn in exactly 1 hour. Keeping the rope alongside length, light one rope at both the ends and the second rope at one end. When the first rope is burnt completely that means half an hour has elapsed (because burnt from both sides, no matter how non-uniform it is, it will burn completely in half hour). When the first rope is finished , light the other end of the second rope. When the second rope is also finished, its 45 minutes time

When the first rope is finished, i.e. half hour has elapsed , the remaining part of rope has to burn in 30 minutes. Now again no matter how non-uniform the rope is ,when burnt from both ends it will take half the time when it is burnt at one end. So the remaining time for the second rope when burnt from both the ends will be 15 minutes. This makes total of 45 minutes

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