Question

Secondary SchoolMath 5 points


The average marks of 39 students of a class is 50. The marks obtained by 40th students are 39 more than the average marks of all the 40 students. Find the mean marks of all the 40 students

Answer 1

Given that average of marks of 39 students is 50

Average = sum of marks of 39 students/39

=> sum of marks/39 = 50

=> sum of marks = 50 × 39

=> sum of marks = 1950


So sum of the marks of 39 students is 1950

Let the marks scored by 40th student be x

So the average would become

(1950 + x)/40

Given that his marks are 39 more than the average of 40 students

=> x = (1950 + x)/40 + 39

=>
$x = \frac{1950 + x}{40} + 39 \\ \\ = > x = \frac{1950 + x}{40} + \frac{1560}{40} \\ \\ = > x = \frac{3510 + x}{40} \\ \\ = > x = \frac{3510}{40} + \frac{x}{40} \\ \\ = > x - \frac{x}{40} = \frac{3510}{40} \\ \\ = > \frac{40x - x}{40} = \frac{3510}{40} \\ \\ = > \frac{39x}{40} = \frac{3510}{40} \\ \\ = > x = \frac{3510}{40} \times \frac{40}{39} \\ \\ = > x = 90$

So the boy scored 90 marks

So average =
$\frac{1950 + 90}{40} \\ \\ = \frac{2040}{40} \\ \\ = 51$

The average is 51

Answer :- 51