Hamir gave Gabriel 2/5 of his cards.

1 - 2/5 = 3/5

Hamir had 3/5 of his cards left.

So 3/5 of his cards = 18 cards

1/5 of his cards 18 ÷ 3 = 6

Cards Hamir gave = 6 x 2 = 12

Part a is correct

Cards that Hamir had at first

= 6 x 5
= 30


Cards that Gabriel would have if Hamir did not give him any

= 109 - 12
= 97

Since Faiz had 24 more than Gabriel, and he gave Gabriel 5/6 of his cards,

We can say Gabriel has 6 units of cards
And Faiz has (6 units + 24) cards

5/6 of Faiz's cards = 5/6 x (6 units + 24)
= 5 units + 20

So Gabriel would have (if Hamir did not give him)

5 units + 20 + 6 units
= 11 units + 20

11 units + 20 = 97

11 units = 97 - 20 = 77

1 unit = 77 ÷ 11 = 7

Faiz had 6 units + 24 at first
= 6 x 7 + 24
= 42 + 24
= 66

Gabriel = 6 units
= 6 x 7
= 42

Hamir = 30

Total = 66 + 42 + 30 = 138

Required fraction

= Faiz/total

= 66/138

= 11/23

Thanks