Suspicion that the deaths may be part of a cover-up have prompted calls for the resignation of Shivraj Singh Chauhan, the Madhya Pradesh chief minister and a senior member of Narendra Modi's governing BJP, which has long held power in the state.
India's opposition Congress party — which was ousted by Mr Modi and the BJP in the 2014 general election in part because of public disgust with years of corruption during its 10-year rule — has described Vyapam as "the biggest and most dangerous corruption scandal in modern India".
In a front-page editorial on Tuesday, Mint, the Indian business newspaper, called for an impartial investigation by authorities from outside Madhya Pradesh. "Even by India's weak standards of law and order, a murderous rampage is on," it said.
More from the Financial Times:
Indian ride-hailing service Ola appoints Arun Sarin to board
India: Land in demand
Bollywood star in hot water over Nestlé noodle row
Methods used in the scam included paying imposters to take exams for candidates seeking to join institutions such as medical colleges, the civil service and the police. The strategy is said to be in use across India and has even been depicted in a Bollywood movie.But the scale and centralized organisation of the scam in Madhya Pradesh was unprecedented, implicating senior officials as well as candidates and the students who impersonated them.
Politicians and commentators say the scandal tarnishes the anti-corruption reputation hitherto enjoyed by Mr Modi and the government among their younger supporters.
However, it could paradoxically strengthen the prime minister's hand within the BJP, given that many of those implicated in this scandal and a concurrent one involving the Indian Premier League cricket tournament are party rivals or opponents.
The corruption "reinforces the image that these [BJP] people are no different from the others", said one senior party member who asked to remain anonymous.
If the mysterious deaths — said by some to number more than 40 and by one Congress politician to exceed 150 — do turn out to be murder, "it would be a new low" in the way India deals with its corruption scandals, the BJP member said. "Even if five or 10 of those 24 or 42 deaths have taken place in unnatural circumstances, it's definitely too many."
Mr Chauhan announced on Tuesday that he was yielding to demands that he request a probe by the India's Central Bureau of Investigation. "I do not want to leave anybody in doubt over our intention to clean the system and punish the guilty," he said on Twitter.
Read MoreIndia stocks lag peers as investors lose patience
Siddharth Varadarajan, one of the founding editors of online news portal The Wire, said such a scandal affecting young job seekers would be "much more viscerally felt by people" than the cricket scandal. "For this cohort, which was a major contributor to Mr Modi's victory, I think for them this is a very big eye-opener.
"The system of recruiting people for government jobs and administering exams is clearly something that provides rich pickings, and it's not surprising that politicians would be involved in that," he added.
The BJP's Uma Bharti, India's water minister and a former chief minister of Madhya Pradesh, said that there was panic in the state over the deaths and that she was traumatized that her name had been mentioned in a statement to police by one of the accused. Denying involvement, she said: "It's a very deep conspiracy. The biggest example of the deep conspiracy is that my name is in it."