IMC 2005 Q22
22. 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?
- A Down by 10%
- B Down by 8%
- C No change
- D Up by 8%
- E Up by 10%
Intermediate Mathematical Challenge 2005, Question 22. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A Down by 10%
Let the number of cases solved in 2003 be \(x\). Then, as this was 80% of the number of cases, there were \(5x/4\) cases to solve in 2003. So the number of cases to solve in 2004 was \(5x/4 \times 6/5\), which is \(3x/2\). Inspector Remorse solved 60% of these cases, that is \(3x/2 \times 3/5\), which is \(9x/10\). So the change in the number of cases solved was a 10% decrease.
Solution © UK Mathematics Trust, from the IMC 2005 solutions.