Given, α and β be two numbers where α<β. ∵ The geometric mean of these numbers exceeds the smaller number α by 12 i.e. √αβ=α+12 ......(i) And the arithemetic mean of the same number is smaller by 24 than the number β. i.e.
α+β
2
=β−24 ......(ii) By solving Eqs. (i) and (ii), we get α=6,β=54 ∴|β−α|=|54−6|=48