"There is a high frequency of ADHD [attention-deficit hyperactivity disorder] symptoms in patients with binge eating/purging eating disorders that motivates further studies."
That was the conclusion reached in the study by Nils Erik Svedlund and colleagues  (open-access) who, among other things, set out to "explore the prevalence and types of self-reported ADHD symptoms in a large, unselected group of ED [eating disorder] patients assessed in a specialized ED clinic." Participants (over 1100 of them) were "seeking help at the Stockholm Centre for Eating Disorders (SCED) from 4 February 2013 through 18 September 2015" and as well as being confirmed to have an eating disorder were also screened for ADHD-type behaviours using the WHO ADHD Self-Rating Scale for Adults (ASRS-screener). Notice the 'self-rated' part of that last sentence...
Based on a ASRS screener score of 14 or above, researchers reported that some 30% of females (N=1094) self-reported 'issues' associated with a diagnosis of ADHD. Some 34% of men included for study (N=47) reported similar ADHD traits (31.3% of the total group including those diagnosed with 'Eating Disorder Not Otherwise Specified (EDNOS) type 5' were on or above the ASRS screener score of 14).
Bearing in mind the presence of various types of different eating disorders in their cohort, researchers also looked at how those self-reported ADHD traits might correlate with sub-groupings. They report that: "The highest frequency of possible ADHD was found in BN [Bulimia Nervosa] and in AN-BP [Anorexia Nervosa bingeing/purging subtype], respectively." They also noted that specific symptoms of ED correlated with the ASRS-screener scores: binge eating, purging, loss of control over the eating and BMI [body mass index] > 17.5. I might add that based on responses to another schedule - the Comprehensive Psychiatric [Psychopathological] Rating Scale (CPRS) - included as part of the study, authors noted something of a link between the ASRS trait scores and "the CPRS scales for depression..., anxiety... and obsession-compulsion." But: "Psychiatric comorbidity correlated to ADHD symptoms without explaining the differences between eating disorder diagnoses."
Keeping in mind that answering 6 questions on a screener questionnaire does not an ADHD diagnosis make, I am rather interested in these and other findings. I am by no means an expert on eating disorder but I have previously been interested in the suggestion that autistic traits may be 'over-represented' when it comes to ED (see here). Combined with the idea that autism and [diagnosed] ADHD might not also be unstrange diagnostic bedfellows (see here) and you can perhaps see that there is potentially more research to do in this area in these times of overlap and ESSENCE. And speaking of ESSENCE ...
With a word or two of caution, I note the authors also talked about potential 'treatment' options given the overlap between ADHD traits (self-reported) and ED. So: "This motivates further randomized trials with stimulant treatment for bingeing/purging ED-patients with and without a concomitant ADHD diagnosis." Certain stimulants have quite a good track record when it comes to ADHD (see here) but the authors rightly note that 'appetite suppression' is a potential side-effect of such pharmacotherapy and something perhaps not ideal if someone is already underweight. More studies are indicated to disentangle what is linked to what.
And while I'm on the topic, the link between autism traits and anorexia nervosa might actually be a little more tenuous that you perhaps think ...
 Svedlund NE. et al. Symptoms of Attention Deficit Hyperactivity Disorder (ADHD) among adult eating disorder patients. BMC Psychiatry. 2017; 17: 19.
 Karjalainen L. et al. Eating disorders and eating pathology in young adult and adult patients with ESSENCE. Compr Psychiatry. 2016 Apr;66:79-86.
 Postorino V. et al. Investigation of Autism Spectrum Disorder and Autistic Traits in an Adolescent Sample with Anorexia Nervosa. J Autism Dev Disord. 2017. Jan 24.
Svedlund, N., Norring, C., Ginsberg, Y., & von Hausswolff-Juhlin, Y. (2017). Symptoms of Attention Deficit Hyperactivity Disorder (ADHD) among adult eating disorder patients BMC Psychiatry, 17 (1) DOI: 10.1186/s12888-016-1093-1