The first restriction site is after 150 base pairs, thus
The second restriction site is 100 base pairs after the first site, so
The third restriction site is: 700 base pairs after the second site, so
The third restriction site wasn't at 1,000 base pairs so it actually split the last piece of DNA into 2 fragments. The last fragment is the last 50 base pairs of the DNA, so
The sum of the fragment lengths adds up to 1,00 base pairs, so we know they are the correct lengths.
I hope this helps!
I notice you actually mentioned the correct answer in your question?
Circular plasmid, 3 restriction sites, so after complete digestion: 3 fragments.
Length of the circular plasmid is 1000 BP, so the total, combined length of all three resulting fragments should be 1000.
Fragment 1: .
First restriction site is at pos(ition)=150 , second at pos=250 , so the difference = 100 BP.
Second restriction site is at pos250 , third at pos950 , so the difference = 700 BP.
You have already cut at all three restriction sites for frags 1 & 2, so the remainder is the third fragment:
1000BP minus 700BP (frag2) minus 100BP (frag1) leaves 200 BP .
This third fragment is 200 BP long, because: 50BP starting from the third restriction site, and OVER pos0 (there is no restriction site there, so no cut ) to Pos150 ...
Which is basically what you mentioned in your question already...