A display of lights contains three different colors of bulbs: red, blue and white. There are equal numbers of each color of bulb. The amount of time that the bulbs stay on can be varied. However, the bulbs always come on according to the following pattern: Red bulbs come on every 2 seconds
Blue bulbs come on every 3 seconds
White bulbs come on every 5 seconds

Initially, the display is set so that all the bulbs flash momentarily when they come on.
All the bulbs flash at the same time at 12:00.

(a) How many more times will all the bulbs flash at the same time before 12:05?

The display is changed so that now the white bulbs stay on for 4 seconds when they come on (and therefore are off for 1 second before coming on again). The red and blue bulbs continue to flash as before. All the bulbs come on at 13:00

(b) What proportion of the bulbs are on exactly 8 seconds after 13:00?

The display is changed again. Now all the bulbs stay on for 1 second when they come on. All the bulbs come on at 14:00.

(c) (i) For how many seconds during the first 30 seconds are no bulbs on?
(ii) For how many seconds during the first 30 seconds are exactly two bulbs on?