Information given:

At the end,

Number of marbles Darius has = 45 marbles

Number of marbles Ellen has = 30 marbles

Number of marbles Farhan has = 25 marbles

Calculations: Let’s say Darius has x number of marbles, Ellen has y number of marbles, and Farhan has z number of marbles at the beginning.

1st round

Darius gave 1/5 marbles to Ellen.

=> Number of marbles Darius has = x – x/5 = 4x/5

Number of marbles Ellen has = y + x/5

2nd round

Ellen gave 1/4 marbles to Farhan

=> Number of marbles Ellen has = (y + x/5) – 1/4 (y + x/5) = 3/4 (y + x/5)

Number of marbles Farhan has = z + 1/4 (y + x/5)

3rd round

Farhan gave 1/2 of his marbles to Darius.

=> Number of marbles Farhan has = 1/2 [z + 1/4 (y + x/5)]

Number of marbles Darius has = 4x/5 + 1/2 [z + 1/4 (y + x/5)]

So, it can be written as,

1/2 [z + 1/4 (y + x/5)] = 25

4x/5 + 1/2 [z + 1/4 (y + x/5)] = 45

3/4 (y + x/5) = 30

Simplifications:

4x/5 + 25 = 45

=> x = 5(45-25)/4 = 25

3/4 (y + x/5) = 30

=> (y + 25/5) = (30)4/3 = 40

=> y + 5 = 40

=> y = 40 - 5 = 35

1/2 [z + 1/4 (y + x/5)] = 25

=> [z + 1/4 (y + x/5)] = 2 (25) = 50

=> z + 1/4 (35 + 25/5) = 50

=> z + 1/4 (35 + 5) = 50

=> z + 1/4 (40) = 50

=> z + 10 = 50

=> z = 50 - 10 = 40

Conclusions:

Darius has 25 number of marbles, Ellen has 35 number of marbles, and Farhan has 40 number of marbles at the beginning.