Aptitude - Average - Discussion

Very simple.

Let no. of. pupil be x.

New mark (wrongly entered) = 83.
Replaced mark (correct mark) = 63.

Increased avg = 0.5(1/2).

Formula: New mark=Replaced mark+(Number of pupil*inc avg).

We can apply this formula for this type of question.

Now,

83 = 63+(x*0.5).
= 83-63 = x*0.5.

= 20 = x*0.5.
= 20/(1/2) = x.
= 20*2 = x.
= 40 = x.

Number of pupils in the class is 40.

Hope it clear your doubts.

Correct mark = 63.
Wrongly entered = 83.

The average marks for the class got increased = 1/2 => 0.5.

A = For single pupil extra mark = 1*1/2 = 0.5.

B = Extra added mark = 83 - 63 => 20.

The number of pupils in the class "X"= B/A.

Therefore x = 20/0.5; 0.5 =1/2.

x = 20/(1/2).
x = 20* 2.
x = 40.

The number of pupils in the class is 40.

Let, average marks of class = x & also let, total no. of pupil in the class = A.

When the mark is 63. Then, the total marks of all pupil = Ax.

When, 83 is entered instead of 63,

Then avg marks of the class = A(x+1/2).

Then, A(x+1/2)-Ax = 83-63.

=> A/2 = 20.

=> A = 40. Option(C).

Let x be the no. of pupil, y is the avg.

63/x = y,

83/x = y+1/2,

By dividing these 2 equations you will get y value. Substitute y in 1st equation, you get x as 40.

Simple.

Let the total marks be x,

Let the total no of students be x, and let the average marks of all the students be x.

Increase in the total marks = 83-63 = 20.

So, total marks/total students = avg marks.

=> x+40/x = x+1/2.

x gets cancelled on both sides of the equation.

Then the remaining terms are,

=> 20/x = 1/2.

=> x = 40.

Average of the total as it is increased by 20 can be written as:

= s+20/n.

= s+20/n = s/n*1/2 (as the original avg is increased by 1/2).

= 2(s+20) = s.

Hence s = 40.

@Midhun J.

You are right. I can so much relate with your answer.

Its very simple given difference of avg is half hence,
(83/x)-(63/x) = 0.5.

Hence by solve x = 40.

let x be the no.of students.
When it is 83, the avg is increased by 1/2.

So we get,
x(avg+1/2) = 83 --(1).

Also given that 63 is the correct mark so we get an equ like,
x(avg) = 63 --(2).

Now (1)-(2)we get,
x(avg)+x(1/2)-x(avg) = 83-63.

Therefore, x/2 = 20.

x = 40.

I hope this helps you all. It's quite easy if u just go step by step according to the question.

Let no.of pupils be x.
Let total marks be y.

Earlier
y/x = Avg...eq(1).

Later
Marks increased by 20 (as 83-63=20) and the average increases by 1/2
Hence,
(y+20)/x = (1/2+Avg)....eq(2).

Now clearly we see the relation in the above 2 equations so hence we try to divide them and let's see what do we get,

Dividing eq(1)/eq(2).

(y/x)*(x/y+20) = (Avg)/(1/2+Avg).

On solving. We get,
y=40*Avg.....eq(3).

No substitute this value of 'y' eq(3) in eq(1).
i.e.,
y/x=Avg....eq(1).

So after putting value of y it becomes,
(40*Avg)/x=Avg.
Hence, x=40.

This is the easiest method I have found so far...