CPE exam: The children agreed to take it in turns to tidy the playroom

Solution 1:

Certainly, in British English you can take it in turns to do something, and you can take turns doing something too.

Both the stated answer and the Original Poster's answer are perfectly grammatical in British English. In fact, the British National Corpus yields more hits for take turns than take it in turns, with 52 hits for the former and 31 hits for the latter (nothing much hinges on this). The BNC contains 100 million words.

However, the Corpus of American English, which contains about 520 million words, has 959 hits for take turns and zero hits for take it in turns.

To take it in turns, therefore, seems to be a very British phenomenon.