It takes 2 hours for a thick candle to burn out = 120 minutes, and it takes 1 hour =60 minutes for a thin candle to burn out.

The thick candle burns for 45 minutes, burning 3/8 and the rest 5/8; The thin candle burns for 45 minutes, burning 3/4, and the rest is 1/4.

The original length ratio of thin candle to thick candle is 5/8: 1/4 = 5: 2.