ANSWER:
3:3:2
EXPLANATION:
We can start by transferring the rate at which D and E split the profit and loss equally.
Since they both get one half, D and E are represented by 1/2 or 50%
The equation for their portions is 1 = D + E
The new partner, F, takes 1/4 of the total profit
1 - 1/4 = F
3/4 = F
Next, we can determine how much of the loss and profits go to D and E
Since D and E are equal, we can sub D in for E
3/4 = D + E
3/4 = D + D
3/4 = 2D
3/4/2 =D
3/4(1/2) = D
3/8 = D
The ratio is 3/8: 3/8: 1/4
To get rid of fractions, multiple everything by 8:
3: 3: 2
Therefore, the ratio of D:E:F is 3:3:2