In which of the following schools is the number students who passed with distinction as a percentage of those students who failed the least?

For this part, we will also have to calculate the number of students who failed in each school. 
adding that to our previous data table we get:

School    Total     Passed    Distinction     Without distinction    Failed
A              800          640            300                      340                   160
B             1050         840            350                      490                   210
C             1200         920            450                      470                   280
D              750          600            260                      340                   150
E              900          750            330                      420                   150
F             1500        1000           450                       550                   500


Calculating the students who passed with distinction as a percentage of students who failed for the given options we see, 
Option A: $$\frac{470}{280}\times\ 100\approx\ 170\%$$
Option B: $$\frac{420}{150}\times\ 100\approx\ 280\%$$
Option C: $$\frac{490}{210}\times\ 100\approx\ 230\%$$
Option D: $$\frac{550}{500}\times\ 100\approx\ 110\%$$

We can see that Option D or School F has the least percentage in this category. 
Therefore, Option D is the correct answer.