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Inspector Remorse had a difficult year in 2004. A crime wave in Camford meant that he had $20\%$ more cases to solve than in 2003, but his success rate dropped. In 2003, he solved $80\%$ of his cases, but in 2004 he solved only $60\%$ of them. What was the percentage change in the number of cases he solved in 2004 compared with 2003?


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This problem is taken from the UKMT Mathematical Challenges.