The total number of students in section P and Q of a class is 130. The number of students in section P is 20 more than that of section q. The average score of the students in Q, in a test, is 40% more than that of students in P. If the average score of all  the students in the class is 114, then what is the average score of the students in P?

97.5

  P + Q = 130

P = 20 + Q

P = 75, Q = 55

40% = \(\frac{2}{5}\)

Avg marks ⇒ P = 5x, Q = 7x

5x × 75 + 7x × 55 = 130 × 114

                   760x = 130 × 114

                        x = \(\frac{130 × 114}{760}\) = 19.5

Avg. score of students in P = 19.5 × 5 = 97.5