Consider that we are having two candles both if start burning from one side totally get burn in 60 mins we can also burn a candle from both side now we have to find a way from which we can measure 45 min with the help of these candle.

Start burning one candle from both side and second candle from one side first candle will finish in 30 min(as burning from both sides) and in same 30 min the half of second candle(as complete can burn in 60 min so in 30 min half will get burn ) will get burn now start burning the second candle from another side and the candle that is left  should get burn in 30 min but burning from both side will take only 15 min to get burn

So first 30 min to burn first and half of second candle and next 15 min to burn another half part of second candle

So, the total time taken is 30+15 = 45 mins

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