This is not permissible as music is haram in Islam and working in a gym that reveals women’s awrah is prohibited as  well.

What is the ruling concerning teaching fitness classes with music? A sister who has become a full time student of knowledge is considering to start to work again as fitness instructor, which she has been doing for the past 15 years, before she converted to Islam, and teach classes with music. (That type of classes can’t be taught without music.) 

Jobs | February 3, 2015 3:09 pm
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I have given 5000000 to someone to do business with this money. He buys land then sell it with profit. He made a deal that he will take 20% from this profit for working while I do nothing and he gives me profit every following year. This is has loss sometimes and sometimes profit is high. Is this permissible?
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I work for a charity organisation in the UK and every year they do a “Christmas Toy Appeal”. Other companies donate toys and then these are distributed to destitute families with young children. I was given the responsibility to arrange which families should receive the toys, but I want to know was it permissible for me to take part in this?