In a class test, four students — P, Q, R, and S — each secured an integer score out of 10 (repetition of marks allowed). The sum of P's marks and the average of the marks obtained by Q, R, and S is 9. The sum of Q's marks and the average of the marks of P, R, and S is 15. The sum of R's marks and the average of the marks of P, Q, and S is 11. It is also known that the sum of P's marks and twice of R's marks is 9. What is the average score of all four students?

The first condition gives P + (Q+R+S)/3 = 9, so 3P + Q + R + S = 27. The second gives Q + (P+R+S)/3 = 15, so P + 3Q + R + S = 45. The third gives R + (P+Q+S)/3 = 11, so P + Q + 3R + S = 33. Adding these three equations yields 5P + 5Q + 5R + 5S = 105, meaning P + Q + R + S = 21. Dividing this total by 4 gives an average score of 6.25.

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