Question

Q26. Division A has 15 students and division B has 20 students. Average score of students in division A is greater by 2 as compared to the average score of students in division B. The total marks of all the students in divi- sion B is 160 more than total marks of all the students in division A. Find the average marks of students in division A

Answer 1

Explanation:

Let a be the total score of Div. A

Let b be the total score of Div. B

given,

`(a)/(15) - (b)/(20) = 2`

as equation 1.

and

`b - a = 160 \\ - a + b = 160`

as equation 2.

Now multiply equation 2 by 1/20 to eliminate b to solve for a.

`( - a)( (1)/(20) ) + (b)( (1)/(20) ) = ( (1)/(20) )(160) \\ - (a)/(20) + (b)/(20) = 8`

take this new equation as equation 3.

now we will use equation 1 + equation 3 to eliminate b to solve for a.

`( (a)/(15) + ( - (a)/(20) )) + ( - (b)/(20) + (b)/(20) ) = 2 + 8 \\ (a)/(60) = 10 \\ a = 60 * 10 \\ = 600`

Div.A total score = 600

Average Score = Total Score / Number of students.

`(600)/(15) \\ = 40`