Two candles have different lengths and different thicknesses. The shorter one would last 11 hours, the longer one would last for 7 hours. But of them are lit at the same time and burn evenly. After 3 hours both have the same length remaining. The ratio of their original lengths is

Let us assume that the first candle burns at a rate of X units per hour, and the second at Y units per hour. 

Hence, the length of the shorter candle is 11X and the longer one is 7Y. 

After 3 hours, the remaining lengths would be 8X and 4Y, which is to assumed as equal in value. 

Hence, 8X = 4Y, which means 2X = Y

We shall substitute this in the initial expressions of length that gives us the length of shorter candle as 11X, and the longer as 14X.

Hence, the ratio of lengths is 11:14.