Let a₁ and d₁ are the first term and common difference of the first AP

and a₂ and d₂ are the first term and common difference of the second AP

Given, the ratio of the sum of the first n terms of two A.Ps = (7n + 1) : (4n + 27)

=> S₁ /S₂ = (7n + 1)/(4n + 27) .................1

=> {2a₁ + (n-1)d₁ }/{2a₂ + (n-1)d₂ } = (7n + 1)/(4n + 27)

Now, T₉ /t₉ = {a₁ + (9-1)d₁ }/{a₂ + (9-1)d₂ }

=> T₉ /t₉ = {a₁ + 9d₁ }/{a₂ + 9d₂ }

=> T₉ /t₉ = {2a₁ + 2*9d₁ }/{2a₂ + 2*9d₂ }

=> T₉ /t₉ = {2a₁ + 18d₁ }/{2a₂ + 18d₂ }

=> T₉ /t₉ = {2a₁ + (19-1)d₁ }/{2a₂ + (19-1)d₂ }

=> T₉ /t₉ = (7*19 + 1)/(4*19 + 27) ....................from equation 1

=> T₉ /t₉ = (153 + 1)/(76 + 27)

=> T₉ /t₉ = 154/103

=> T₉ : t₉ = 154 : 103

So, ration of 9th term of AP is 154 : 103