Answer:
 The amount of income assigned to the two partners would be $18,100 and $19,900 respectively. 
Explanation:
For computing the amount of income assigned to the two partners, we have to do the following calculations which are shown below:
1. Dividend amount for each partner:
For Fred = Invested amount × rate of return
               = $20,000 × 15%
               =$3,000
For Barney =  Invested amount × rate of return
                   = $32,000 × 15%
                   = $4,800
The total dividend amount equals to
= Fred dividend + barney dividend
= $3,000 + $4,800
= $7,800
2. Now compute the remaining amount, and divide it in the sharing ratio
So, the remaining amount would be 
= Partnership income - total dividend amount
= $38,000 - $7,800
= $30,200
So the Fred income would be = $30,200 × 50% = $15,100
And, the barney income would be = $30,200 × 50% = $15,100
So, the amount of income:
For Fred = Dividend income + remaining income
               = $3,000 + $15,100
               = $18,100
For Barney = Dividend income + remaining income
                    =$4,800 + $15,100
                    = $19,900
Hence, the amount of income assigned to the two partners would be $18,100 and $19,900 respectively.