Aamir Khan was 51 when he played the role of a 19 year old boy in Dangal .
From Bollywood Life article
So Aamir Khan has done it again what he does the best.
The PK actor has gone through a drastic makeover for his upcoming film, Dangal, in which he will be seen going through three different stages for he will play the role of a 19-year-old, 29-year-old and 55-year-old.
Below is the image of him as 19 years old.
Another example, Amitabh Bachchan was 67 years old when he played the role of a 12 year old boy suffering from a rare genetic disorder called progeria in Paa . From Wikipedia plot summary , Auro (Amitabh Bachchan) is an intelligent and witty 12-year-old boy with an extremely rare genetic disorder called progeria.
Mentally he is twelve and very normal, but physically he looks five times older.
Though, in this case, the character he played was supposed to look like an old man.
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Shirley Henderson was around 37 when she played Moaning Myrtle in the Harry Potter movies.
Born 1965, appeared in Harry Potter and the Chamber of Secrets which came out in 2002 and Harry Potter and the Goblet of Fire which came out in 2005.
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Stockard Channing (born 1944) played teenager Rizzo in Grease (1978) at the age of 34.
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Robert Redford was 48 when The Natural was released.
Granted he played a 35 y/o for most of the movie, but he plays a 19 y/o pitcher on a way to a tryout in the prologue.
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Ferris Bueller's sidekick Cameron was played by 29-year-old Alan Ruck in Ferris Bueller's Day Off .
Alan Ruck was born in 1956, and appeared as Ferris Bueller's trusty high-school friend Cameron in the 1986 movie Ferris Bueller's Day Off .
Mr. Ruck was probably not 30 during filming, since movies are always shot months or even years before they are released.
*Thanks to Joe for the comment on the original question that led to this answer.
( Fun fact:
I've bumped into Alan Ruck twice in my grocery store in Studio City, CA.
He even said "hi" once because he could see how star-struck I was.)
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There is a very popular Mexican comedy TV show named " El Chavo del Ocho " (1972-1979), in which all the characters are played by adults even when they are playing children's roles.
I understand that some people may consider it a parody, but truly it is not.
It may be actors portraying children, but they are not parodying them: within the El Chavo's universe they are not pretending to be children, they are children.
Roberto Gómez Bolaños (aka Chespirito) was the creator/writer/producer/director of the show, and he also played El Chavo, an 8-year-old boy who escaped from an orphanage and lives in the apartment #8.
Chespirito was born in 1929, and the show concluded in 1979.
So in the last season, he was an 50-year-old man portraying an 8-year-old boy (42 years difference).
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Here's one from Japan: The lead role in My Love Story! , a major production from a major studio, was played by Ryohei Suzuki .
The character is 15 years old throughout (no flashbacks or early life scene setting), but at that time Suzuki was 32 years old, so a 17 year difference.
(I've also just thought -
The Curious Case of Benjamin Button:
Brad Pitt was 44 when he played BB at 12 years old - I can't remember if he appeared at an earlier age, though)
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Wet, Hot American Summer
(the Netflix show not the film) had multiple actors in their 40's and early 50's portraying teenage and early 20's characters.
Granted
this was part of the joke, but for your question this should work (unless you would qualify this as parody).
For example, Michael Showalter was 45 when the series was filmed.
And he has confirmed they are indeed teens here :
"We thought it was funny that in the original we played a bunch of thirty year olds playing teenagers.
Now we're in our forties and our characters are even younger," Showalter said in a statement.
If not the show, then the movie, which was not done to the absurd level as the show would still count.
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This example will be very hard to beat for anyone who cares about historical accuracy.
In the 10 May 1980 episode of Fantasy Island
My Fair Pharaoh/The Power
the "My Fair Pharaoh" part had the protagonist going back in time to meet her hero Queen of Kings Cleopatra VII Philopator.
Cleopatra's brother and enemy King Ptolemy XIII Theos Philopator (62/61 BC to 47 BC) was portrayed by Michael Ansara (born 15 April 1922, died 31 July 2013) who was thus aged 58 years and 25 days when the episode aired and was probably 43 or 44 years older than Ptolemy and 3.8 to 4.07 times as old as Ptolemy when filming his scenes.
This is an example of a middle aged man portraying a character arbitrarily depicted as an adult despite being one of the most famous child rulers in history!
So this could be the extreme example depending on whether you go by Ptolemy's historical age or his unspecified adult fictional age in the episode.
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Although he is not the oldest in these answers, he is playing a fairly younger role in Hannah Montana .
Jason Earles plays his role as a 15 years old kid, and can you believe he was on his 30s?
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Though he also appears as an elderly version of the character in the framing story at the beginning and end of the film, (then) 40-year-old Martin Short played a 10-year-old in Clifford .
The film was a comedy, and the casting of an adult actor in the role of a young child was surely intended to be humorous, but it's never specifically highlighted as a joke in the film--it's played more or less straight.
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If we take the premise of the movie The Curious Case of Benjamin Button , then Brad Pitt born 1963 played a teenager in 2008 at some point or another in that movie.
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There's a common trope in Hollywood where  teenagers are played by adult actors . But which TV show or movie set the absolute record in terms of the age difference between the role and the actor? To clarify:   The character played must be a teenager, so younger than 20 years old  The portrayal is done in a serious manner - not as a parody, or a "what if" clip, or a dream, etc  It must be a live action film or a TV show
Who was the oldest actor to play a teenager?
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<trope>
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Many adult actors have played teenagers in films including Aamir Khan, Amitabh Bachchan, Shirley Henderson, Stockard Channing, Michael Ansara and Brad Pitt. There are plenty of actors who have played the role of youngers.
There are plenty of actors who have played the role of youngers.