Quiz shows are actually much cheaper than regular scripted shows. For the BBC specifically, they released [this document](http://downloads.bbc.co.uk/commissioning/site/tariff_prices_for_independents.pdf) covering how much certain types of shows cost. Quiz shows are in the “low-cost entertainment” category. Almost 20 times cheaper to produce than premium dramas.
So the answer to your question is really just “The same way other shows get their money.”
For the BBC that’s mostly the TV license, but for ITV where both of the shows you listed air it’s mostly advertising.
As someone pointed out, game shows are relatively cheap to produce. They’re in a fixed location, only have to pay 1-2 actors, regular schedules, not live.
As for revenue, depending the market the ad is shown in, according to ITV itself, it can cost up to 13k, per 30 second advert.
That’s prime time London though, realistically maybe a bit less since it’s on later and may have less of a ratings draw. Either way, it’s several thousand per commercial. The questions are weighted and written so only X amount of people win every few episodes as well.
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