If an article is sold at 12.5% gain instead of 16 2/3 % loss, the man…

16\(\frac{2}{3}\)% (Loss) = \(\frac{1}{6}\)

CP : SP₁ = 6 : 5      ............(i)

12\(\frac{1}{2}\)% (Profit) = \(\frac{1}{8}\)

CP : SP₂ = 8 : 9      ............(ii)

Comparing (i) and (ii)

SP₁ :  CP  :  SP₂  = 20 : 24 : 27

ATQ,

⇒ 27R - 20R = 1533

⇒ 7R = 1533

⇒ 1R = 219

So, C.P. = 24 × 219 = 5256, and

S.P. @10% profit = 5256 × \(\frac{110}{100}\) = 5781.6