There are increasing number of families have private cars.
修改：There are increasing number of families （that）have private cars.
欢迎提问,乐意解答；愿你满意, 望你采纳.所以说原句没有语病吗？继续回答：原句有语病，加上that才行。我将that加上括号，表示是修改意见。欢迎追问，乐意解答；愿你满意, 望你采纳。