A salesman sells two kinds of trousers: cotton and woollen. A pair of cotton trousers is sold at $30\%$ profit and a pair of woollen trousers is sold at $50\%$ profit.
The salesman has calculated that if he sells $100\%$ more woollen trousers than cotton trousers, his overall profit will be $45\%$. However, he ends up selling $50\%$ more cotton trousers than woollen trousers.
What will be his overall profit?
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