The question is asking for the ratio, s, of the original lengths of the two candles.

Let x = initial length of the short candle

And y = initial length of the long candle

Their rates of burning:

Length = rate time

Or,

rate = length / time

For x, since it will burn for 20 hrs,

rate = x/20 (units of length)/hr

After 5 hrs burning, what is left is

x -(x/20)(5)

= x -x/4

= 3x/4 units of length

For y, that will burn out after 14 hrs,

rate = y/14 (units of length)/hr

After 5 hours burning, what is left is

y - (y/14)(5)

= (14y -5y)/14

= 9y/14 units of length

Those two leftovers are equal in length, so,

3x/4 = 9y/14

Cross multiply,

42x = 36y ------(i)

we are looking for ratio s ......which can be x/y or y/x.

Say we get s = x/y

Divide both sides of (i) by y,

42x/y = 36

x/y = 36/42 = 6/7

Therefore, s = x/y = 6/7 --------------answer.