The first novel Hastings appears in is The Mysterious Affair at Styles (1916), where it is possible to estimate that he was born in 1886, and although age is never discussed for this character, it is possible to say he is thirty at this time.
In Murder on the Links (1923) he falls in love with Dulcie Duveen – encouraged by Poirot. Hastings then acquires a ranch in Argentina where he lives for some time. The exact age of many characters in Agatha Christie works is not mentioned, but it is possible to add 7 years to Hastings age by Murder on the Links – making him 37.
In The Big Four (1927) Hastings is given a message that his wife has been kidnapped in Argentina by The Big Four.
In The A.B.C. Murders (1936) Returning from South America, Arthur Hastings meets with his old friend, Hercule Poirot, at his new flat in London.
In Curtain Captain Hastings joins Poirot, he is recently widowed and a father of four grown children, including Judith the youngest.
Although published in 1975, Curtain was written some thirty years earlier, so it is not easy to place an exact age on Poirot or the other associated characters.
The link between the last few books is Sleeping Murder (1976) which is set during WW2, specifically September 1940 and May 1941. So, we do have a period of time to consider when it comes to trying to understand the age of some of Christie's characters. However, it is possible to see that Hastings has aged by 18 years. So, for Curtain time setting, add on a few more years. Hense, Judith, the youngest of Hastings children can be seen as an adult.