In Vikas Swarup's novel Q&A (which Slumdog Millionaire is based on) there's no Latika. The protagonist simply recounts his life story, in a series of largely unrelated vignettes, explaining how he came to know the answer to each question he encountered on Who Wants to be a Millionaire.
But screenwriter Simon Beaufoy has explained that he created the character of Latika to bring to his adaptation a certain continuity that the novel lacked, using a love story to anchor the plot. And the inclusion of Latika is essential to the film; Slumdog Millionaire simply wouldn't be Slumdog Millionaire without its magnetic muse. (Source)
The Long, Hard, And Not Very Fun Journey of the Third Musketeer
We catch our first glimpse of Latika in the opening minutes of the film. She's a radiant blast of color and light amidst the hustle and bustle (and drabness) of the train station. From this moment, however brief, Latika has captured our imagination; Jamal can't seem to shake that image of her, and neither can we.
Though we don't know for certain, Latika was probably orphaned in the Bombay riots, much like Jamal and Salim. And given their similar age and experiences, the "three musketeers" develop a tight bond, working together to survive on their own – that is until they meet Maman. When Jamal and Salim are able to successfully escape from the gangster, but Latika is recaptured, it appears that their roads have split for good.
As the story then focuses on Jamal and Salim for the next several years of their lives, we don't know for certain what happens to Latika. But when Jamal decides to return to Mumbai to find her, he learns that she has become Maman's "prized possession." Ooh. That doesn't sound good.
Known by the name of "Cherry," it is implied that Latika has been kept a virgin to increase her value for her eventual sale into prostitution. (Yeesh.) Jamal and Salim are able to find and escape with Latika, but the reunion doesn't last long, as Salim, now jacked up on testosterone from killing Maman, decides that it's his turn to take ownership of Latika.
After this moment, we lose track of Latika all over again. But through some crafty sleuthing, Jamal's able to hunt her down, discovering that she is now a trophy of slumlord Javed Khan. When the two are finally able to meet in Javed's compound, Latika is incredibly reluctant to leave with Jamal, explaining that "it is too late," and that Jamal has to forget about her.
But it's clear that this decision has more to do with Javed's ruthlessness—"he'll kill us both," Latika says—than her feelings for her childhood friend.
Despite her concerns, she attempts to escape anyway… although her plan is thwarted by Salim, who runs her down and captures her in the train station. For this transgression, she receives a pretty nasty cut on her cheek.
It isn't until the end of the film that she's able to escape a second time—this time successfully, thanks to Salim, who, in a change of heart, gives Latika his car keys and cell phone and tells her to go after Jamal:
SALIM: Go. Just drive. There won't be another chance.
LATIKA: He will kill you.
SALIM: I'll take care of him.
Thanks to his sacrifice, Latika is able to escape captivity once and for all. As a result, Latika and Jamal are finally able to reunite safely, and live out their lives together in peace.
Damsel In Distress? Or Dissident In… Control?
Okay, we'll say it; plot-wise Latika really doesn't do that much. She doesn't even get that much screen time. She spends most of the story essentially in captivity, getting tossed around from one obnoxious slumlord to the next, so Jamal can have something to do for most of the movie in tracking her down.
In this sense, her character has been criticized as a damsel in distress, lacking any real agency of her own: she's merely waiting for her knight and shining armor to rescue her:
LATIKA: You came back for me.
JAMAL: Of course.
LATIKA: I thought you'd forgotten.
JAMAL: I'd never forget. Not for one moment. I knew I'd find you in the end. It's our destiny.
Oh yeah, and let's address the other elephant in the room; she is the only major female character in the movie. In fact, she's the only female character who shows up for more than three scenes. There's Jamal's mother, who barely makes it fifteen minutes into the film. There's that one producer on Who Wants to be a Millionaire, who speaks literally one word. And then there's Latika. That's it.
But maybe there is more to Latika than we're giving her credit for. She's faced unconscionable hardship in her life, but has managed to persist and survive all the same. As a young girl, she is sexualized and objectified, exploited and abused. And as she grew into womanhood, those realities only intensified. In this sense, Jamal, nor Salim, could have any idea what she has gone through.
Tough As Nails
And that's where the tough cookie part of Latika's character begins to show: she might have used her sexuality to her advantage, using what little agency she had to create a relatively safe and comfortable life for herself… even if it is among brutal gangsters. Maybe her character really embodies quiet strength and perseverance rather than powerlessness and passivity.
So is Latika yet another example of a token love interest with no mind or agency of her own, simply a prop to push the plot forward? Or is she actually one of the toughest characters in the entire story, showing remarkable strength and perseverance in the face of repeated abuse and exploitation and using what power she has as a woman to survive?
You could certainly make a case either way. But it's difficult to argue against the fact that Latika's presence, however limited, infuses in Slumdog Millionaire a certain passion and emotional richness… as well as making the movie super-duper romantic and warm fuzzies-inducing.