Let $T$ be the total acres of the cocoa farm. Step 1: Calculate the fraction of the farm given to the wife and the first child. The wife received $\frac{2}{5}$ of the acres. The first child received $\frac{1}{3}$ of the acres. The combined fraction received by the wife and the first child is: $$ \frac{2}{5} + \frac{1}{3} = \frac{2 \times 3}{5 \times 3} + \frac{1 \times 5}{3 \times 5} = \frac{6}{15} + \frac{5}{15} = \frac{11}{15} $$ Step 2: Calculate the fraction of the farm remaining for the other three children. The remaining fraction of the farm is $1 - \frac{11}{15}$: $$ 1 - \frac{11}{15} = \frac{15}{15} - \frac{11}{15} = \frac{4}{15} $$ This $\frac{4}{15}$ of the total farm was shared among the three children in the ratio $3:5:2$. Step 3: Determine the total parts in the ratio and the value of one part. The sum of the ratio parts is $3 + 5 + 2 = 10$ parts. The child who had the least share corresponds to the smallest part in the ratio, which is 2 parts. We are given that the child with the least share received 8 acres. So, 2 parts = 8 acres. Therefore, 1 part = $\frac{8 \text{ acres}}{2} = 4 \text{ acres}$. Step 4: Calculate the total acres shared among the three children. The total acres shared among the three children is 10 parts: Total acres for three children = $10 \times 4 \text{ acres} = 40 \text{ acres}$. Step 5: Calculate the total acres of the farm ($T$). We know that the 40 acres represents $\frac{4}{15}$ of the total farm $T$. $$ \frac{4}{15} T = 40 \text{ acres} $$ To find $T$, multiply both sides by $\frac{15}{4}$: $$ T = 40 \times \frac{15}{4} $$ $$ T = 10 \times 15 $$ $$ T = 150 \text{ acres} $$ i) The total acres of the man left (meaning the total acres of the farm) is $\boxed{\text{150 acres}}$. Step 6: Calculate the number of acres the wife received. The wife received $\frac{2}{5}$ of the total acres $T$. $$ \text{Wife's acres} = \frac{2}{5} \times 150 \text{ acres} $$ $$ \text{Wife's acres} = 2 \times \frac{150}{5} \text{ acres} $$ $$ \text{Wife's acres} = 2 \times 30 \text{ acres} $$ $$ \text{Wife's acres} = 60 \text{ acres} $$ ii) The number of acres the wife received is $\boxed{\text{60 acres}}$.