Step 1: Under the IMNCI fast-breathing cut-offs, a child aged 2 months to 12 months has fast breathing if the respiratory rate is 50 per minute or more. This infant is 3 months old with a rate of 52 per minute, so fast breathing is present.
Step 2: Apply the classification. Fast breathing without chest indrawing and without danger signs is classified as pneumonia, so option b is correct.
Step 3: No pneumonia (option a) requires the absence of fast breathing. Severe pneumonia (option c) needs chest indrawing, which is absent here. Very severe disease (option d) needs danger signs such as inability to feed, convulsions, or stridor at rest, none of which are present.