The effective dose by inhalation or ingestion is going to depend on what somene inhales or ingests. Someone in an area of relatively high radon concentration will get a correspondingly relatively high effective dose due to inhalation. Someone in an area where drinking water contains relatively high concentrations of radium will correspondingly high effective dose due to ingestion. The total annual effective dose and the relative proportions due to inhalation, ingestion and external radiation will therefore be variable with location and the particular local sources of radiation exposure.
In regards to children and infants there are two factors to consider. First, the majority of dose from ingestion or inhalation is due to alpha and beta radiation, relatively none-penetrating and therefore giving a higher dose to the surface of organs than to deeper parts of the organ. In infants and children the organs are smaller, hence have a larger surface area per unit mass and will hence absorb a greater amount of energy per unit mass of the organ. More energy per unit mass = larger dose. The second factor is that organs in infants and children are still growing and developing. Cell damage in developing organs is more likely to lead to cancers. The effective dose rate combines the energy deposition rate (Gy) with a weighting factor relating to likely health effects of exposure to specific organs. Children and infants will receive a larger dose rate (µGy/h) and that will have more potential effect on health - hence a larger effective dose rate (µSv/h).
Effective dose by inhalation or ingestion depends upon the radionuclide and its chemical form. An insoluble radionuclide may have a larger dose by inhalation because it will remain in the system longer than an ingested dose that passes through. A soluble radionuclide may be distributed through the body differently by ingestion than by inhalation.
The question did not include radionuclide or chemical form so no answer is possible to the question without more specific information.
The case for infants is the same, not enough information on radionuclide and chemical form.
The answer concerning surface area of organs is correct only if the radionuclide is restricted to the organ surface. Some radionuclides are distributed evenly through an organ, but others go to specific volumes of the organ. Most dose models assume even distribution through the organ. This question can only be answered for a specific organ, the radionuclide, and the chemical form of the radionuclide.
The answer concerning dose rate to children and infants needs expansion.
Dose to organs (Gy) is the average energy deposited in the organ divided by the organ mass. Dose rate (Gy/h) depends on the total radionuclide deposited in the organ for beta and alpha radiations. If the radionuclide per unit mass is the same in an adult and an infant the dose rate is the same. The total dose to the adult will be larger than the total dose to an infant, but the average dose per unit mass will be the same. So, the average dose to the organ will be the same for infant and adult. Average dose and dose rate to the infant and adult organs are the same. There is a case where this might not be true. The model for the infant organ may be different from that of the adult. The average dose and dose rate will be different over time. The total dose to the organ is the integral of the average dose rate per unit mass over time. This is not total energy deposited in the organ, but mean energy deposited per unit mass.
Energy deposited (Gy) in the organ is not the same as risk to the organ or the effective dose (Sv). The units are the same (J/kg) but Sv is based on a model interpretation of risk. The same average dose to an infant organ might be modeled as a larger risk than the same average dose to an adult organ.
The effective dose to an infant organ may be different from the effective dose to an adult organ because the energy deposition models to the organ are different, the risk model to the organ are different, or both.
The ratio of radiation dose from inhalation and ingestion depends on countries. For example, according to the data in 2005-2008, the approximate ratio was 4 on the world average, 5 in US and UK, and 3 in Japan (Figure XXXVi on page 404 of Volume I, Annex B of the UNSCEAR Report 2008 available at http://www.unscear.org/docs/publications/2008/UNSCEAR_2008_Annex-B-CORR.pdf ). The inhalation dose comes mainly from radon-222 and -220 in air, and depends on the types of materials of houses/buildings, time spent inside houses/buildings, etc. The ingestion dose comes mainly from potassium-40 in food, and for instance, depends on the types and quantity of food.