Another challenge!Question:-In a class of students, the average(arith

1.	Another challenge!Question:-In a class of students, the average(arithmetic mean) of the test scores is 70.In another class of students, the average of the scores for the same test is 92.When the test scores of two classes are combined, the average of the test scores is 86.Find .
Answer» $\large\underline{\sf{Solution-}}$ Case 1 Number of STUDENTS in class = p Average score of p students = 70 Case 2 Number of students in class = N Average score of n students = 92 Combined score of p + n students = 86 So given data is represented as For class 1 $\bf :\longmapsto\:n_1 = p \: \: \: and \: \: \: \overline{x_1} \: = \: 70$ and For class 2 $\bf :\longmapsto\:n_2 = n \: \: \: and \: \: \: \overline{x_2} \: = \: 92$ Now, we KNOW that Combined mean is given by $\:\bf :\longmapsto\:\overline{X} = \dfrac{n_1\overline{x_1} + n_2\overline{x_2}}{n_1 + n_2}$ $\rm :\longmapsto\:86 = \dfrac{70 \times p + 92 \times n}{p \: + \: n}$ $\rm :\longmapsto\:86p + 86n = 70p + 92n$ $\rm :\longmapsto\:86p - 70p = 92n - 86n$ $\rm :\longmapsto\:16p = 6n$ $\bf\implies \:\dfrac{p}{n} = \dfrac{3}{8}$