Is this an eating disorder?

The person eats very little. She eats about a third of what I eat. (But she is a woman). She also eats very slowly and takes about 3-4 times as long as I do to eat. She is 165 cm tall and now weighs 41 kg. A year ago she weighed 48 kg. Unlike people with anorexia, she does not feel too fat; rather, she recognizes that she is too thin and wants to gain weight. But she really has a hard time eating. Sometimes she wants to eat something certain and then she refuses to eat anything else. What is the name of the type of eating disorder she has? Is the weight she has reached critical? What can be done to help her gain the weight back? I am very worried.