If toll tax is devised in such a way that total cost of travel remains same irrespective of the path then what is the minimum cost of travel from X to Y?

From the given condition ,
cost incurred in path 2 is equal to that in path 3 then T₃ = 0
Similarly ,equating cost of path 3 and path 4 T₇ = 0
Equating cost of path 4 and path 5 we will get
260 + T₆ + T₈ = 230 + T₅
⇒ T₅ = T₆ + T₈ + 30
Equating cost of path 1 and path 2 we will get ,
240 +T₁ = 260 + T₂+ T₄
or T₁ = T₂ + T₄ + 20
For minimum total cost T₁ = 20 and T₅ = 30 then cost incurred is Rs 260.
Therefore , the minimum cost of travel from X to Y is Rs 260 .