(A) Incorrect. For the problems highlighted above.

(B) Correct. This option corrects both the problems in the original sentence. I believe both ‘to estimate’ and ‘estimating’ are correct.

(C) Incorrect. For the following reasons:

1. Both the problems of the original sentence.
2. Given the change in the order of the information, the emphasis in the sentence has shifted. In the original sentence, the emphasis is on ‘estimating being a difficult problem’. In this option, the emphasis is on ‘lack of a single yardstick’. The emphasis in the original sentence makes more sense.

(D) Incorrect. For the following reasons:

1. In the structure ‘X is a difficult problem’, the emphasis is on X. In the structure, ‘a difficult problem is X’, the emphasis is on identifying a difficult problem. In the context of the sentence, it makes sense to emphasize ‘X’. Thus, the construction in this sentence is inferior to that in option B.
2. The construction ‘a single yardstick is lacking’ is inferior to the construction ‘there is no single yardstick’.
3. The modifier ‘by which all…measured’ is separated from the noun ‘yardstick’ by the verb.

(E) Incorrect. For the following reasons:

1. First problem of option D.
2. The part after ‘because’ is an inverted sentence. After converting into the regular form, it becomes ‘all distances cannot be measured by a single yardstick’. However, this gives a meaning different from that of the original sentence. This construction seems to eliminate even any future possibility of such a single yardstick. It says that measuring all distances by a single yardstick is impossible. However, the original sentence meant that currently there is no single yardstick by which all distances can be measured. The meaning of the original sentences looks more reasonable.

If you have any doubts regarding any part of this solution, please feel free to ask in the comments section.