Two students X and Y appeared in a test. The score of X is 20 more than that of Y. If the score of X is 75% of the sum of the scores of X and Y, then what is the ratio of score of X to score of Y?

Explanation

Let Y's score be a. Then X's score is a + 20. We are given a + 20 = \frac{75}{100}(a + a + 20). Solving this: a + 20 = \frac{3}{4}(2a + 20) \Rightarrow 4a + 80 = 6a + 60 \Rightarrow 2a = 20 \Rightarrow a = 10. X's score = 30. Ratio = 30:10 = 3:1.

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