A firm is selling two products, chairs and barstools, each at $50 per unit. Chairs have a variable cost of $25 and barstools $20. Fixed cost is $20,000.
If the sales mix is 1:4 (1 chair for every 4 bar stools) what is the break even point in sales? In units of chairs and barstools?

What is the best way to calculate break even point here? I have two different solutions that check out?

Solution1:
using a weighted approach
BEP Sales =
20000/((((50-25)/50)*0.75)+(((50-20)/50)*0.25))=38,095.25
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Units= 38,095.25/50 = 761.90
Chairs = 761.90 * .25 = 190.48
Bar Stools= 761.90*.75 = 571.42

Solution2:
Revenue=(50*5)=250
Combined VC = (20*4)+25=105
BEP=20000/(250-105)=137.93
Sales=137.93*250=34,482.76
Chairs=137.93
Bar stools= 137.93*4=551.72

Your second solution hits the correct answers. Having a fixed mix of 1:4 lets you think of this one in terms of 'packages', with each package consisting of 1 chair and 4 stools. Each package has a unit sales price of 250, and a unit variable cost of 105.

I haven't vetted your first solution in detail, but at a glance it looks like you're trying to weight the chairs:stools at 25:75 instead of 20:80. Fix your weights accordingly and both of your approaches will probably agree.

__________________
...it was early and I was full of no coffee...

Aweseome, that did it.
20000/((((50-25)/50)*0.2)+(((50-20)/50)*0.8))=

=34483

Units = 689.6552
Charis=units*.20 = 137.31
Barstools = units*.80=551.72