You have to recognise that by giving away money to Jane,

1. Kenneth loses a sum of money.
2. Jane gains the same sum of money.

From "Kenneth had $90 more than Jane" to "Jane had $30 more than Kenneth", there is a total "money flow" of $120.

So Kenneth must have given away $60 to Jane. The order of sequence is in the following two-step story.

1. After Kenneth gives away the $60 (but Jane has not accepted the money yet), Kenneth has $30 more than Jane.

2. After Jane accepts the $60, Jane has $30 more than Kenneth.

Makes sense, right?

So Kenneth gives $60 to Jane. This corresponds to 60% of his money.

60% --> $60
1% --> $1
100% --> $100

So Kenneth starts out with $100.
Jane starts out with $10.

You can check that the answers are true by making sense of the story using these numbers.