Let x be the number of pairs of running shoes on display.
Then, 1.5x is the number of pairs of walking shoes on display.
The total number of pairs of shoes is x + 1.5x = 2.5x = 135.
So, x = 135 / 2.5 = 54.
Therefore, there are 54 pairs of running shoes and 1.5(54) = 81 pairs of walking shoes on display.
The answer is option B: 54 pairs of walking shoes and 81 pairs of running shoes.