Ken has 90 marbles at first.
Rahman has 48 marbles at first.

So Ken has 90 - 48 = 42 more marbles than Rahman at first.

Since they each gave away the same number of marbles, Ken will continue to have 42 more marbles than Rahman.

Therefore, (4 unit - 1 unit = 3 units)

3 units - 42 marbles
1 unit - 14 marbles

After giving away, Rahman has 14 left. So he gave away 48 - 14 = 34 marbles.

(Check:

Ken has 4 units (14x4 = 56) marbles left.
56 + 34 = 90 (tallies with how much he had at first).

Therefore they each gave away 34 marbles.