How much longer does it take the sun's light to reach Pluto at apogee than at perigee? How would I express that in a ratio?

It takes about 2 hours 42 minutes longer for the sun to reach Pluto at its furthest distance from the sun than it would take when Pluto is at its closest point (within Neptune's orbit) to the sun.

Pluto's orbit varies from 2.776 billion miles to 4.584 billion miles from the sun. Since light travels at nearly 700 million miles per hour, it takes about 4 hours 9 minutes to reach it when close, and 6 hours 51 minutes when farthest. In order to get the ratio of times, it is easiest to divide 4.584 by 2.776, yielding about 1.65, that is, it takes the sunlight 1.65 times longer to reach it when furthest than when closest.

first a note... although it is technically ok to use perigee and apogee in this case, it is more correct to use perihelion and aphelion. Pluto is 4435.0x10^6 to 7304.3x10^6 km away from the sun. the ratio of the time it takes light to travel these two distances is simply the inverse of the ratio of the distances. so it takes light 1.6470 times as long to reach pluto at aphelion.

if you want to get the time it will take for light to travel each of these distances, you simply divide the distance by the speed of light:

4435.0x10^6 km / .29979x10^6 km/s = 14794 sec = 4 hrs, 6 minutes, 34 sec
7304.3x10^6 km / .29979x10^6 km/s = 24365 sec = 6 hrs, 46 min, 5 sec