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What is The earliest indicator of response after starting iron in a 6–year–old girl with iron deficiency is – and explain in detail?
The reticulocyte count is the first to rise. This is followed by elevation of haemoglobin levels. body iron stores are restored after correction of haemoglobin levels.
`Rise in Reticulocyte count occurs by the second or third day. This is followed by elevation of haemoglobin levels.
Body iron stores are repleted after correction of haemoglobin levels. - Ghai

Thus Rise in Reticulocyte count → Rise in Haemoglobin Restoration of iron stores ferritin 
Time Span

Within 1 day (24 hours)
Within 2 days (48 hours)
Within 2-3 days
Up to 2 months
Still later

Responsible with the start of iron therapy

The child becomes less irritable
Appetite improves
Initial bone marrow response
Reticulocyte count increases
Restoration of haemoglobin levels
Restoration of iron stores (Ferritin levels)