The plot of the film re-introduced the "lost and reunite" formula to Bollywood, originally featured in the 1943 Ashok Kumar-Mumtaz Shanti-starrer Kismet. A happy family separated by waqt (time) goes through a series of trials trying to reunite. The film was later remade in Telugu as Bhale Abbayilu (1969) and in Malayalam as Kolilakkam (1981). The film contains the Hindi songs "Hum Jab Simat Ke", sung by Mahendra Kapoor and Asha Bhosle, "Waqt se din aur raat", sung by Mohammed Rafi, "Aage Bhi Jaane Na Tu", sung by Asha Bhosle and "Ae Meri Zohra Jabeen", sung by Manna Dey, composed by Ravi and picturised on Balraj Sahni and Achala Sachdev.
Lala Kedarnath Prasanta (Balraj Sahni) has three sons whose birthdays are on the same day. On the occasion of their birthday celebration, they are visited by a well-known astrologer, who advises Lala Kedarnath not to be proud for his past achievements and to not be too optimistic about the future as the act of time (waqt) is unpredictable. Lala Kedarnath ignores the prediction and is busy making plans for an even wealthier future. Later that night, as he is proclaiming his grand plans for the future to his wife, Laxmi (Achala Sachdev), there is a sudden earthquake and the whole town crumbles. When Lala Kedarnath regains consciousness, his house has been destroyed and his family is gone.
The oldest son, Raju, ends up in an orphanage, while the middle son, Ravi, is found on the streets by a rich couple who take him to their home to raise him as their own son. The youngest son, Vijay, who is still an infant, is with his mother. Unable to find the rest of the family, Laxmi and Vijay live in poverty. Lala Kedarnath traces Raju to the orphanage, but finds that he has run away because the orphanage manager (Jeevan) beat him. Frustrated, he kills the manager and is jailed. As the police drive away with Lala Kedarnath, the audience sees young Raju running in the streets and turning into an adult (Raaj Kumar).
Raju grows up as Raja, a sophisticated thief, who works for Chinnoy Seth (Rehman). Raja falls in love with Meena (Sadhana Shivdasani) and decides to give up the life of crime. To his dismay, he realises that Meena intends to marry Ravi (Sunil Dutt), who is a family friend. On the night before their engagement, he decides to kill Ravi, only to realise that Ravi is his long-lost brother. Before he can ask Ravi about his parentage, Meena's parents decide to break off the engagement upon discovering that Ravi is of unknown parentage and religion.
Heartbroken, Ravi leaves home after an argument with his foster sister, Renu (Sharmila Tagore), over his objection to her affair with Vijay (Shashi Kapoor), who is working as a chauffeur for Chinnoy Seth. Renu has been in love with Vijay since their college days together, but Vijay has not been able to find a suitable job in Mumbai despite having a BA degree. Laxmi has been diagnosed with stomach cancer. To pay for her medical expenses, Vijay has no other option but to be a driver.
Raja learns about Ravi's problem and decides to reveal the truth about their relationship at a party organised by Chinnoy Seth. However, Chinnoy Seth's employee Balbir Singh (Madan Puri) drunkenly misbehaves with Meena at the party and Raja manhandles him. Later that night, the drunk Balbir gets into a fight with Chinnoy Seth and in self-defense, Chinnoy Seth ends up stabbing Balbir fatally with his dagger. To cover up his crime, he decides to frame Raja and drags the body to Raja's house, hiding it in his closet. Vijay happens to witness this but is shut up with the promise of money for his mother's treatment.
Raja is arrested and asks Ravi to defend him as an advocate, while Vijay initially testifies falsely and then recants his statement after being confronted. Lala Kedarnath also appears in court as the witness who found Raja being caught by the police. Raja is ultimately proved innocent and Chinnoy Seth is convicted after he blurts out the truth in court, thanks to Ravi. Afterward, Laxmi arrives in the court to make sure Vijay did the right thing. Lala Kedarnath sees her in the courtroom and has an emotional reunion with her and Vijay. Raja then overhears Lala Kedarnath narrating his orphanage incident to Laxmi and introduces himself and Ravi as Lala Kedarnath and Laxmi's remaining two sons. The entire family finally reunites. In the end, Lala Kedarnath and the rest of the family build a new home where they, Meena's family, and Renu's family live together.
