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

Step-by-step explanation:

Let a be the total score of Div. A

Let b be the total score of Div. B

given,

$\frac{a}{15} - \frac{b}{20} = 2$

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.

$( - a)( \frac{1}{20} ) + (b)( \frac{1}{20} ) = ( \frac{1}{20} )(160) \\ - \frac{a}{20} + \frac{b}{20} = 8$

take this new equation as equation 3.

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

$( \frac{a}{15} + ( - \frac{a}{20} )) + ( - \frac{b}{20} + \frac{b}{20} ) = 2 + 8 \\ \frac{a}{60} = 10 \\ a = 60 \times 10 \\ = 600$

Div.A total score = 600

Average Score = Total Score / Number of students.

$\frac{600}{15} \\ = 40$