Maybe I am a bit of a square, but I agree with @Eoink who got this one really quickly.
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Well spotted, I wrote the final term under the product and carelessly added rather than subtracted. 
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I’m going to write this next one exactly as I saw it a few weeks ago.
Three brothers entered a shop, each needing a pair of shoes resoled and a key cut. There are two assistants in the shop, both of whom work at the same speed. It takes 5 minutes to resole a pair of shoes and 5 minutes to cut a key.
How quickly can they finish ?
It didn’t take long to work out the answer, which i’m sure was correct, but …!!
15 minutes I think. It seems a bit too simple, so I may be missing a subtlety.
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I get 15 minutes too. I’m stuck on the others, I thought 24 was the right answer…
Hi Mike, I’ll let Ravvie and/or Eoink explain the answer to 4; 5; 7; 9; 13; 15; 19; 21; ?
if they don’t wish to do so, I’ll explain what’s going on.
So did I. That makes three of us so far. And as far as I can see, we are all correct, however …
Ravvie spotted it first, but to help Mike out, if you subtract 2 from each number in the sequence you get 2,3,5,7,11,13,17,19, it’s the primes.
ditto with the 443546
And that one is that each term is the previous term squared minus 10.
Another series:
3, 4, 8, 9, 14, 23, 25, 31…
What is the next number and why?
Well, technically, the brothers may be able to re-sole shoes… or cut keys…
however…
the answer given in the book is 
30 minutes (one assistant does 1 pair of shoes and 3 keys, the other does two pairs of shoes)
So, the real puzzle (unintended by the author, it was probably just a typo !!) is … what should the wording of the initial puzzle have actually been ?
15 minutes per pair of shoes and 5 minutes per key.
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Exactly, Eoink.
Simple typo … 5 instead of 15, but it leaves you floundering.
A bit like the primes plus two. I get 25 each time I look at it. However, the newspaper gave the right explanation, but quoted 24 !
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36, if my Greek is right.
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It seems that I failed to get you running round in circles.
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314159265 3589793238 might help others who haven’t yet sussed what all this talk of Greek Circles is about.
Note: I have removed the usual decimal point, to hopefully eliminate some possible confusion. And the break between 5 and 3 is deliberate, given Eoink’s extension to 36.
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I think I’ll settle for a beer…
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Best idea Mike !
The numbers that I wrote are basically Pi.
Starting with 3, progressively add numbers to generate Ravvie’s teaser.
Eg 3, then 3+1=4; then 4+4=8; then 8+1=9; etc
Hope this helps you Relax and enjoy the beer Even more
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