Aptitude - Average - Discussion

Its simple,

Let us assume that the total number of pupils in class be x+1,

Now Let the sum of the marks of x students (whose marks have been entered correctly be S) , and let original average be A, then (S+63)/(x+1) = A; Equation 1.

And (S+83)/(x+1) = (A+1/2); Equation 2.

Divide Equation 1 by Equation 2;

(S+63)/(S+83) = (2*A)/(2*A+1) ;

Solving it, we get: S+63=40*A; Equation 3.

Now, put value of Equation 3 in Equation 1, we get:

(40*A)/(x+1) = A;

Solve it, we get: x+1=40.

And we have assumed the total students to be x+1. Hence total students = x+1 = 40.

83-63/(1/2) = 2*20 = 40.

Let as take, m is actual total marks of students and p is number of the pupil.

Difference between average = 1/2.
m/p - (m+20)/p = 1/2.
p = 40.

But the question says increased by half, so shouldn't it mean the incorrect average was increased by half of the correct average?

Thanks in advance

I too have that same doubt @Maria Ninan.

Can anyone clarify it?

Let suppose average marks A.
Number of students be X.

If the marks entered correctly i.e. 63 then.

A = (Total_1) / X -----------> (1).

Total_1= A * X -------------> (2).

If the marks entered is wrong, ie 83 then,

A+ (1/2) = (Total_2) /X -----------> (3).
Total_2 = [A + (1/2)] * X-------------> (4).
Total_2 = A * X + X/2 -----------> (5).

And the difference between Total_1 and total_2 is (83 - 63 = 20).
Therefore Eq (5) - (2).

A * X + X/2 - A * X = 20.
X/2 = 20.
X = 40.

The Correct average increased by half.

Once read the question, it's stated that. Instead of 83, it's wrongly entered as 63.

Now. As we know sum/num=avg ------->1 (when mark entered is correct).
83 - 63 = 20. This is the new difference when the mark is entered wrongly.

So, sum+20/num=avg+avg (1/2) ------->2 (when mark entered is the wrong Avg is increased by 1/2).

Sum + 20/num = avg (1 + 1/2).
Sum + 20/num = avg (3/2).

Substituting 1 in 2;

Sum + 20/num = sum/num (3/2).
Sum + 20 = 3/2sum.
Sum = 40.

(83 - 63) = 20,

X * 20 = 1/2,

= 40.

Avg = sum * total number.
1 if all are correct then the eqn is,
avg = sum/number.
sum = avg * number----> 1st eqn.

2 if wrong 83 instead of 60 then eqn is,

sum + (83 - 63) = (avg + 0.5) * number.
sum = (avg + 0.5) * number - 20----> 2nd eqn.

let divide 1st eqn by 2nd eqn.
sum/sum = 1.

Avg * number = (avg + 0.5)number - 20.
In solving this avg canceled by avg, So, avg - avg = 0.

0.5 - (20/number) = 0
0.5 * number = 20
Number = 20/0.5
Number =40