There are two candles. Both will only burn exactly for an hour. How will you use these two candles to measure forty-five minutes?

Burn one candle from both the ends and simultaneously burn the other candle from just one end. In half an hour, the first candle would have been burnt fully and the second one would have been burnt half. Now light the other end of the second candle as well. In this way, the second candle will take only half the time (30/2 = 15) to burn fully.

Thus, you will have measured forty five minutes.