correct answer is: a) 129.46 and 70.54

Explanation

Let, one part is ‘x’
Another part is \left(x-58.92\right)
According to the question,
x+\left(x-58.92\right)=200
\rightarrow x+x-58.92=200 _{[remove bracket]}
\rightarrow 2x=200+58.92 _{[interchange]}
\rightarrow 2x=258.92
\rightarrow x=\large\frac{258.92}{2}
\rightarrow x=\large\frac{25892}{2\times100} _{[remove decimal]}
\rightarrow x=129.46
\therefore One part is =129.46
And, another part is \left(x-58.92\right)
\rightarrow\left(129.46-58.92\right)
\rightarrow 70.54
Ans: Two parts are 129.46 and 70.54.

An alternative way to phrase this particular math query is possible:

1. How to divide 200 into two parts with a difference of 58.92?
2. What are the two numbers that add up to 200 with a difference of 58.92?
3. Splitting 200 into two parts with a difference of 58.92?
4. Solving for two numbers that differ by 58.92 and sum up to 200?