How old were Joseph & Mary when they marrried?

That nun should have been the first person to ask ... but perhaps the question has just occurred to user6941 ...

Please note that this does not belong to "Sacred deposit" of the faith (the depositum fidei).

For the age of Mary when she was married, please see this one possible source: VII. MARRIAGE OF THE BLESSED VIRGIN TO JOSEPH in The Life of the Blessed Virgin Mary, [Bl.] Emmerich, Anne Catherine (1774-1824).

If Joseph was 17 and Mary 14, chances are that this was NOT Joseph's second marriage.

Whence comes the stories that this was a second marriage for Joseph, that Joseph was an old man when he married Mary, that the brothers and sisters of Jesus were the children of Joesph from his other marriage etc?

These come from apocryphal writings and perhaps with good intentions, i.e., in attempt to explain the perpetual virginity of Mary.

Please see: Marriage in St. Joseph | New Advent.

Please see: The Perpetual Virginity of Mary (Jerome) | New Advent. Please note that St. Jerome argues that St.Joseph also remained virgin, and this to me, makes sense.

Please see:

• Code of Canon Law, Can. 1083 §1. A man before he has completed his sixteenth year of age and a woman before she has completed her fourteenth year of age cannot enter into a valid marriage.
• cf. Prohibited Marriages and Illegitimate Children under Marriage| Jewish Virtual
  

  The minimum age for marriage under Jewish law is 13 for boys, 12 for girls; however, the kiddushin can take place before that, and often did in medieval times. The Talmud recommends that a man marry at age 18, or somewhere between 16 and 24.

Good day to ask and answer this question, being the Feast of the Nativity of Mary (9 months after the Solemnity of the Immaculate Conception if you're counting)

You know the Bible doesn't have this info in it from the other answers and 2 minutes of poking around. The Bible (in Isiaiah) does prophecy that the Virgin (or at the very least a young woman) will bear a Son, so Mary's not old.

The Apocrypal Gospel of the Nativity of Mary says:

And so she [Mary] reached her fourteenth year; and not only were the wicked unable to charge her with anything worthy of reproach, but all the good, who knew her life and conversation, judged her to be worthy of admiration. Then the high priest publicly announced that the virgins who were publicly settled in the temple, and had reached this time of life, should return home and get married, according to the custom of the nation and the ripeness of their years.

and of Joseph

Now there was among the rest Joseph, of the house and family of David, a man of great age:

which isn't very specific, but I'd imagine it's over 50 at the youngest.

Now, I don't like to think of Joseph as an old man, but it's an old tradition and can't be readily discounted. It's not necessary that James and Jude be half-foster-brothers of Jesus. They could also have been sons of Clophas

Near the cross of Jesus stood his mother, his mother's sister, Mary the wife of Clopas, and Mary Magdalene.

who depending on the interpretation of the commas is also named Mary or not named. I can't tell which, I always thought there were three women, each named Mary at the Cross, but actually reading the Bible is always very surprising. I thought there was also a Salome there. But that's what I read in "Joseph: the man closest to Christ" which is a good book for diving in to all the conflicting traditions concerning young parent Joseph and old parent cherry tree pickin Joseph.

Still, it stands to reason that St. Joseph wasn't that old when he married Our Lady because he brought Jesus up as a "carpenter's Son". He wasn't a long dead obscurity at the time of Our Lord's preaching. The Gospels don't specifically mention that Jesus did carprentry, but that he did practice His father's craft is one of those pseudo-traditional bible inferences people like to make. But even so, carpentry back then (according to Steve Ray in an interview I heard him give more than once on EWTN and Relevant Radio) was more like Stone Masonry than woodwork nowadays. It would have been really, really hard labor and Joseph and Jesus would have had to walk for miles and miles from Nazareth to get to where their work is. And, the reason I'm writing this is just because if, he did work with Jesus, when Jesus was of age (say 14-15, I think), then St. Joseph ,although he was the best man to swing a hammer in human history, probably would have had a rough time doing it into his 60's.

So, best guess. Our Lady was 14-15, her most chaste spouse was 18-25.

One common source of knowledge about Joseph and Mary is the Protoevangelium of James. This non canonical gospel was actually composed some time in the 2nd century AD. It is very known in most churches, including oriental churches. Of course, it is of dubious source, but it has been well known and illustrated in whole Christianity.

9. And Joseph, throwing away his axe, went out to meet them (= the Mary's parents); and when they had assembled, they went away to the high priest, taking with them their rods. And he, taking the rods of all of them, entered into the temple, and prayed; and having ended his prayer, he took the rods and came out, and gave them to them: but there was no sign in them, and Joseph took his rod last; and, behold, a dove came out of the rod, and flew upon Joseph's head. And the priest said to Joseph, You have been chosen by lot to take into your keeping the virgin of the Lord. But Joseph refused, saying: I have children, and I am an old man, and she is a young girl. I am afraid lest I become a laughing-stock to the sons of Israel. And the priest said to Joseph: Fear the Lord your God, and remember what the Lord did to Dathan, and Abiram, and Korah; how the earth opened, and they were swallowed up on account of their contradiction. And now fear, O Joseph, lest the same things happen in your house. And Joseph was afraid, and took her into his keeping. And Joseph said to Mary: Behold, I have received you from the temple of the Lord; and now I leave you in my house, and go away to build my buildings, and I shall come to you. The Lord will protect you. Source

I have seen this episode in the decoration of lot of old churches, in Europe. Even if we do not have to trust it as part of the Holy Revelation - it is by no way a canonical scripture - I usually have no difficulty to follow this representation.

Also consider what "old" means. It is a relative concept. Today, we could say that someone is old when he/she reaches its 70th birthday. But in ancient times, health was much weaker, and we usually married as young as possible. At Joseph's era, the life expectancy was around 20–30! So one may see himself as an "old man", even a widower with grown children... and being 35...

This is also the earliest text that explicitly claims that Joseph was a widower, with children, at the time that Mary is entrusted to his care. This feature is mentioned in a known Origen's text, who adduces it to demonstrate that the 'brethren of the Lord' were sons of Joseph by a former wife.