都正确。
take turns to do (正。不定式作目的状语)
take turns doing (正。现在分词作伴随状语)
take turns doing sth The students were taking turns reading aloud. 学生们正在轮流朗读。
take turns in doing sth BrE 【英】We took turns in pushing the bike along. 我们轮流推自行车。
take turns to do sth Dan and I usually take turns to cook. 我和丹通常轮流做饭。
(以上均摘自《朗文高级英语应试词典》)