West Lothian based Sibbald Training directed the teenagers to a firm that then used the youths to work on a home job for their mentor.
An MSP described the revelations as "outrageous", while the public body responsible for the scheme has ordered an investigation.
First introduced in 2002, the Get Ready for Work initiative is targeted at so-called NEETS – 16 to 19 year olds not in employment, education or training.
Funded by quango Skills Development Scotland to the tune of £25.8 million, private-sector training firms are paid to "place" young people with local companies to enhance their skills and employability.
The teenagers receive £55 a week for taking part and can graduate to an apprenticeship or a job.
According to the Scottish Government website, GRFW provides young people with "confidence" and "transferable skills".
But serious questions are now being asked about the monitoring of a scheme that has been lucrative for the private training companies hired by SDS, such as Sibbald.
The Sunday Herald can reveal that Airdrie-based David Blair, a placement officer at Sibbald, channeled two teenagers on the programme to his son's firm, DCB Fabrication.
The son asked the trainees to help him lay his father's red-brick drive, a job he had been hired to undertake.
Mr Blair confirmed the arrangement to this newspaper when approached at his home last week, but denied there was anything wrong with the way he used GRFW.
But John Speirs, Sibbald's project manager, said: "At the very worst it was naive of David to let his son use the trainees. I can see how that can be perceived as 'too close' in hindsight.
"I said to him, 'the boys can't work on your drive'. It wouldn't be perceived as correct."
He said trainees would not work on the properties of Sibbald staff in the future, adding: "We are a very reputable company. We've got nothing to hide."
Sibbald Training has a contract with SDS to deliver 123 GTFW "opportunities" in this financial year.
According to its website, the company has won a string of national training awards.
The case raises the question of whether there are other examples of trainees being used for the benefit of training company staff.
It is also another setback for government in its bid to tackle the scourge of youth unemployment.
The UK Government policy of encouraging the jobless to take up unpaid work placements was halted after it got savaged in the media.
Labour MSP Neil Findlay said: "These are shocking revelations. Whenever someone questions a Scottish Government training programme we are told that we are talking down our young people, yet here we have trainees doing questionable activity just a few miles from the Minister Angela Constance's front door.
"This is a serious case that needs a thorough investigation by SDS. We need training that gives young people hope for the future, not training that takes money to exploit those who need a start in life."
John Wilson, an SNP MSP for Central Scotland, said: "This situation is outrageous and reminiscent of the failed YTS schemes of the 1980s. SDS must carry out a root-and-branch investigation to ensure the example identified is not the tip of the iceberg and is an isolated case.
"Every young person must be assured that the training being provided can genuinely lead to meaningful employment and not just a cheap labour or a free scheme for employers and individuals."
A spokeswoman from Skills Development Scotland (SDS) said: "We were made aware of this incident earlier this week and ensured that any young people involved were withdrawn from the placement pending an investigation by Sibbald into the circumstances.
"SDS is reviewing this specific case and its wider contract with Sibbald in line with our compliance and quality assurance processes. Our priority is to ensure that young people gain the accredited skills they need to enter the labour market and pursue sustainable careers."
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