The scores achieved by P and Q in an examination are in a ratio of 9:4 respectively. If Q scores an additional 11 points, then P's score will be approximately 25% higher than Q's score. What is the difference between the actual scores of P and Q?

Solution

Let the scores of P and Q be 9x and 4x respectively, based on the ratio 9:4. When Q scores an additional 11 points, his new score is 4x+11. It is given that P's score is 25% higher than Q's new score: 9x=1.25×(4x+11) Solving the equation: 9x=5x+13.75 4x=13.75 x=3.4375 Calculate the actual scores: P =9x = 9×3.4375=30.9375 Q=4x=4×3.4375=13.75 The difference between their scores: 30.9375−13.75=17.1875 So, the difference between the actual scores of P and Q is approximately 17.188