Aptitude - Average - Discussion

According to the property of Average, if each quantity is increased by certain valu "X" then the new average is increase by X.

Now in the question, it is given that average has been increased by 1/2 due to the marks entered wrongly. Therefore we can say that the marks of each n every student should increase by 1/2 as per the property.

Let x be no of students.
Therefore (x *1/2) = x/2.
Now, increase value = 83 - 63 = 20.
Therefore x/2 = 20.
x = 40.

Let x be the sum of marks of all the students except the incorrect mark. and y be the no of students.

Now,

Avg mark of all the students with correct mark =(x+63)/y.
Avg mark of all the students with incorrect mark =(x+83)/y/

Acc to the ques;
(x+83)/y= (x+63)/y+1/2,
(x+83)/y= (2x+126+y)/2y. (taking LCM of denominators)
2(x+83)= 2x +126+y,
2x+166 = 2x+126+y,
y= 40.

Average = total marks/number of pupils.

Average=x+63/number of pupils -------------> (1)
1.5 average=x+83/number of pupils ---------> (2)
eqn(2)-eqn(1).
0.5 = 20/number of pupils.
Number of pupils =20/0.5,
The number of pupils = 40.

Avg = total marks/No. Of pupil.
1/2 = 20/x,
X = 40.

1/2 means 0.5.

Because of difference of 20 this avg 0.5 is increased.
So distributing 0.5 equally to get total 20.

We divide 20/0.5 will give no.of student.
i.e. 20/0.5 = 40 student.

I am not understanding this, please explain it.

Simply:

x = num of pupils.
y = total average.

Therefore,
Total marks of class=xy
Total marks of class due to wrong entry = xy-63 + 83.

New average of class due to wrong entry = (xy-63 + 83)/x
Also, (according to question) new average = y+0.5 (or y+1/2)
Thus, we get:

(xy-63+83)/x = y + 0.5,
x = 40.

Let x be the cumulative marks excepting the wrongly entered mark.
Let y be the no of pupils,
(x+83)/y = ((x+63)/y) + 0.5.
x+83 = x+63+0.5y,
20 = 0.5y,
y = 40.

s= other student.
n = number of student.

avg (when its 83) = avg(when its 63)+1/2.
(s+83)/n = (s+63)/n + 1/2,
(s+83)/n = [(s+63) + 0.5n]/n,
s+83 = s+63+0.5n,
83 = 63+0.5n,
0.5n = 83-63,
n = 20/0.5.
n=20.

Increased by half is old + 1/2 not (1.5 * old).