Question

Why you have to apply more force in moving a cycle which is punched

Answer 1

simply because to maintain the shape of the Tyre
by air filled in the tyre, it would maintain it's shape and the area contacted with ground will be uniform,
but if the tyre is punctured then it's shape will loose and thus the uniformity, the area of contact will be more with the ground and so we would put more force to cycle it