Question

In a class of a boy of a marks 60 was replaced by another boy of marks 80 and the average of the class is increased by 1 mark. Find the strength of the class

Answer 1

Answer:

There are 20 students in the class

Step-by-step explanation:

Formula used:

$Mean=\frac{\Sigma{x}}{n}$

Let number of students of the class be 'n'

$Average=\frac{\Sigma{x}}{n}=p(say)$

$\Sigma{x}=np(say)$

$corrected\:\Sigma{x}=np-60+80(say)$

$corrected\:\Sigma{x}=np+20(say)$

Now,

$New\:average=p+1$

$\frac{corrected\Sigma{x}}{n}=p+1$

$\frac{np+20}{n}=p+1$

$np+20=n(p+1)$

$np+20=np+n$

$n=20$

Answer 2

Answer:

20 students

Step-by-step explanation:

Let the average marks of the boys be 'a' and total number of students be 'b'

Then

average marks =  total marks/number of students

a = Total marks/b

Total marks = ab  

Now one of the marks 60 is replaced by 80

Total marks = ab - 60 + 80

                    = ab + 20

Total number of students remain the same = b

New average is increased by 1 = a + 1

Hence

a + 1 = (ab + 20)/b

ab + b = ab + 20

b = 20

Hence number of students in the class = 20