Question

In a class of p students, the average (arithmetic mean) of the test scores is 70. in another class of n students, the average of the scores for the same test is 92. when the scores of the two classes are combined, the average of the test scores is 86. what is the value of p/n

Answer 1

First case:

average of test score =70

number of students =p

total score of 'p' students = ( average of test score)*( number of students)

total score of 'p' students =70p

Second case:

average of test score =92

number of students =n

total score of 'n' students = ( average of test score)*( number of students)

total score of 'n' students =92n

total number of students = p+n

total average score =86

so, total score =86(p+n)

total score = total score of 'p' students +total score of 'n' students

$86(p+n)=70p+92n$

now, we can simplify it

$86p+86n=70p+92n$

$86p-70p=92n-86n$

$16p=6n$

now, we can find p/n

$\frac{p}{n}= \frac{6}{16}$

$\frac{p}{n}= \frac{3}{8}$................Answer