Why did persphone have to live with hades for 7 months and with demeter on earth for 5 months(in greek myths)

She ate three pomegranate seeds.

Explanation:

Pomegranates are food of the underworld. Since she ate three seeds she has to live with hades for 3 months of the year. For that three months Demeter her mother roams the Earth making plants and crops die, and harsh weather occurs. Winter comes for 3 months and when Persephone returns summer, spring and autumn come.