Verified answer

[tex] \bf \: Solution:[/tex]

Let the younger brother be A and elder be B

[tex] \bf \: Given[/tex]

[tex] \sf \: 5.5 \: years \: ago, A : B = 4 : 5[/tex]

[tex] \sf \: 2.5 \: years \: late, A : B = 6 : 7[/tex]

[tex] \bf \: Calculation[/tex]

Let the age of A 5.5 years ago = 4x

The age of B 5.5 years ago = 5x

[tex] \bf \: According \: to \: the \: question,[/tex]

[tex] \sf(4x + 5.5 + 2.5)/(5x + 5.5 + 2.5) = 6/7[/tex]

[tex] \sf :\implies 7(4x + 8) = 6 (5x + 8)[/tex]

[tex] \sf :\implies 28x + 56 = 30x + 48[/tex]

[tex] \bf :\implies 2x = 8[/tex]

[tex] \bf :\implies x = 4[/tex]

∴ Present age of younger brother = 4x + 5.5 = 4 × 4 + 5.5 = 21.5 years