How Long Did Noah Live?
Question

Did Noah (peace be upon him) live for 950 years, and why does it state in the Quran that he lived for one thousand years (sanah) less fifty years (‘am)? Is there a difference between the words sanah and ‘am (both mean “year”)?
Praise be to Allah.Lessons from the life of Prophet Noah
There are important lessons to be learned from the life of Prophet Nuh (Noah, peace be upon him). 
He lived for many centuries that he spent among his people, calling them to Allah, may He be exalted, feeling compassion for them lest He punish them, hoping that He would bestow His mercy upon them. He never felt despair or wanted to give up; rather he hoped that Allah would guide them at his hands, no matter how long it took. The years of his life offer lessons for callers, teachers and educators in patience, determination and faith. 
His life also offers lessons to all people, so that they may understand that death will inevitably come, no matter how long one lives, and that one’s life is no more than a series of days that end with sunset every day, so as to conclude the story of his soul that was given an opportunity to attain eternal happiness in Paradise, so what a victory it is if it strove to attain this happiness, and what a loss it is if it fell short and was heedless. 
Ibn Abi’d-Dunya narrated in az-Zuhd (no. 358) with his isnad from Anas ibn Malik (may Allah be pleased with him) that he said:
“The Angel of Death came to Noah (peace be upon him) and said: O longest-lived of the prophets, how did you find this world and its pleasures? He said: Like a man who entered a room with two doors, and he stood in the middle of the room for a brief moment, then he went out of the other door.”
How long did Noah live?
The discerning Muslim is the one who pays attention to these lessons and develops the determination and resolve to strive. He should not be preoccupied with the details of history which the revelation did not highlight or explain, and for which there is no sound proof or Shar‘i evidence. 
That includes asking about the age of Noah (peace be upon him). There were several scholarly opinions concerning it among the early generations of the Sahabah and Tabi‘in, but there is nothing proven concerning it in the Quran or Sunnah, such that we could be certain that one of these opinions is correct. However, we will quote these opinions here for the sake of increasing knowledge of what is narrated in the books of the early generations: 

950 years. This is the view of Qatadah. It says in Tafsir al-Quran al-‘Azim by Ibn Kathir (6/268): 

“Qatadah said: It was said that his entire lifespan was one thousand years less fifty; he remained among them for three hundred years before he began to call them, and he called them for three hundred years, and after the Flood he lived for another three hundred and fifty years.”
A similar report was narrated by Ibn Abi Hatim in at-Tafsir, no. 18041 

1050 years. This was the view of Ibn 'Abbas. It was narrated that Ibn 'Abbas (may Allah be pleased with him) said:

“Allah sent Noah (as a prophet) when he was forty years old, and he remained among them for one thousand years less fifty, calling them to Allah; after the Flood he lived for another sixty years, until the people increased in numbers and spread out.”
In ad-Durr al-Manthur (6/455), as-Suyuti attributed it to Ibn Abi Shaybah (7/18), ‘Abd ibn Humayd, Ibn al-Mundhir, Ibn Abi Hatim, Abu’sh-Shaykh, al-Hakim (9/251), who classed it as sahih, and Ibn Mardawayh. 

1020 years. This was the view of Ka‘b al-Ahbar. Ibn Abi Hatim narrated in at-Tafsir (no. 18043): Abu Zur‘ah told us: Safwan told us: al-Walid told us: Abu Rafi‘ Isma‘il ibn Rafi‘ told us: from Zayd ibn Aslam, from ‘Ata’ ibn Yasar, from Ka‘b al-Ahbar, concerning the words of Allah, “and he stayed among them a thousand years less fifty years” al-'Ankabut 29:14]: After that, he lived for another seventy years. 
1400 years. This was narrated from Ibn 'Abbas, and was also the view of Wahb ibn Munabbih. See: Tafsir al-Qurtubi, 13/332 
1650 years. This was the view of ‘Awn ibn Abi Shaddad. It was narrated that ‘Awn ibn Abi Shaddad said: 

“Allah, may He be blessed and exalted, sent Noah to his people when he was three hundred and fifty years old, and he called them for one thousand years less fifty years, then after that he lived for another three hundred and fifty years.” Narrated by Ibn Abi Hatim in at-Tafsir (no. 18044); al-Tabari in Jami‘ al-Bayan, 20/17 

1700 years. This was the view of ‘Ikrimah. It was narrated that ‘Ikrimah (may Allah be pleased with him) said: 

“The age of Noah (peace be upon him) including the time before he was sent to his people and after he was sent was one thousand, seven hundred years.”
In ad-Durr al-Manthur (6/456), as-Suyuti attributed it to ‘Abd ibn Humayd. 
Ibn Kathir said in Tafsir al-Quran al-‘Azim (6/268), after stating that the previous views were odd: “The view of Ibn 'Abbas is more likely (to be correct).”
The difference between sanah and `am
The commentators also differed concerning the reason behind the use of the words sanah and ‘aam (both meaning “year”). There are two opinions: 
1. Some of the commentators are of the view that it is a stylistic reason only, because repeating the same word is heavy on the tongue, so a different word was used the second time, namely ‘am, to make it lighter. 
Az-Zamakhshari said in al-Kashshaf: 
“If you say: why is the word sanah used the first time and the word ‘am used the second time? I would answer by saying that repeating the same word in a single phrase should be avoided in the interests of eloquence, unless that is done for a purpose, such as for emphasis or exaggeration or highlighting a point, and the like.”
Something similar is mentioned in at-Tahrir wa’t-Tanwir, 20/146 
2. The word sanah (year) is used to highlight the difficulty of the years that Nuh (peace be upon him) spent calling his people. They were years of paucity in terms of goodness, rain and blessing (barakah), and in terms of the difficulty that Nuh (peace be upon him) encountered in calling his people, as they responded by turning away and persecuting  him. Then after the flood and the destruction of kufr on earth, he spent years of abundance and ease. The Arabs refer to times of drought and famine as sanah and times of ease and plenty as ‘am. 
Ar-Raghib al-Asfahani said in Mufradat Alfaz al-Quran (2/140): 
The ‘am is like the sanah (both words mean “year”) but the word sanah is often used to refer to the year in which there is hardship or drought. Hence a drought is called sanah. The word ‘am refers to a year in which there is ease and plenty. Allah says (interpretation of the meaning):
“Then thereafter will come a year (‘am) in which people will have abundant rain and in which they will press (wine and oil)” [Yusuf 12:49]
“and he stayed among them a thousand years (sanah) less fifty years (‘am)” [al-‘Ankabut 29:14]. 
Burhan ad-Din al-Biqa'i said in Nazm ad-Durar (14/404): 
“The word sanah is used to refer in a negative manner to the days of kufr (disbelief)… and He said “ ‘am” to highlight the fact that after they (the disbelievers) were drowned, Nooh’s life became one of ease because of the faith of the believers and the abundance of the earth.”
Imam az-Zarkashi said something similar in al-Burhan fi ‘Ulum al-Quran, 3/386 
“Some of the scholars put these two opinions together because there is no reason why these two opinions cannot be regarded as complementary. When it comes to opinions of the commentators – so long as they do not contradict one another – they may all be adopted, which is preferable to rejecting some of them.”
Ibn ‘Adil said in al-Lubab, 12/429: 
“Here I paid attention to a subtle point, which is that different words for “year” are used. In the first case it says sanah and in the second case it says ‘am, lest the wording be too heavy (and so that the words will flow more easily on the tongue). Moreover, the word ‘am is used specifically with regard to the fifty years, so as to highlight that when the prophet of Allah (blessings and peace of Allah be upon him) was rid of them, he enjoyed good times after that. The Arabs refer to abundance by saying ‘am and to drought by saying sanah.”
Please see also the answers to questions no. 10470  and 10551
And Allah knows best.