Step 1: Concept of equal profit-sharing ratio.
When three partners agree to share profits equally, the ratio must distribute the profit into three equal parts.
Step 2: Division of 1 into three equal parts.
If total profit = 1, dividing equally among three partners:
\[
\frac{1}{3} : \frac{1}{3} : \frac{1}{3} = 1:1:1
\]
Step 3: Eliminate wrong options.
- Option (B) $4:1:2$ is unequal.
- Option (C) and (D) appear confusingly written, but the only correct equal ratio is $1:1:1$.
Step 4: Conclude.
Hence, the equal profit ratio for three partners is $1:1:1$.
Final Answer:
\[
\boxed{1:1:1}
\]