The age at which 'Senior' concessions are granted is entirely at the discretion of the body selling tickets. Many will choose 60 as the relevant age (because, up until recently, women got their state pensions at 60 and the same age is then used, for concessionary purposes, for both men and women). However other bodies most choose different ages.
You've posted in 'Sport', so I'm guessing that you're referring to ticket sales at a sporting venue but we'd need to know which one it is in order to seek (and hopefully provide) a definitive answer for you.