Step 1: Understanding the Concept
Protein-energy malnutrition has two forms: kwashiorkor and marasmus.
Step 2: Symptoms
Loss of subcutaneous fat, prominent ribs, dry skin and atrophy of digestive glands in a one year old infant are signs of marasmus.
Step 3: Compare the options
Kwashiorkor shows oedema, nephritis is a kidney disease and cretinism is a thyroid disorder.
Final Answer:
The child is suffering from marasmus.
\[ \boxed{\text{(B) }\text{Marasmus}} \]