Let's denote Ganesh's age as G. According to the given information, Jane is 15 years older than Ganesh, so Jane's age can be represented as G + 15. Additionally, Jane is four times as old as Ganesh, so we can write this as G + 15 = 4G.
Solving the equation G + 15 = 4G, we find that G = 5. Therefore, Ganesh is 5 years old.
Substitute G = 5 into Jane's age equation, Jane's age is G + 15 = 5 + 15 = 20 years old.
Therefore, Ganesh is 5 years old and Jane is 20 years old.