Aptitude - Average - Discussion

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.

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.

(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

Thanks for your explanation @Nik.

Let the number of pupils = x.
Avg of mistaken marks = 83/x,
Avg of correct marks = 63/x,

By question;
83/x = 63/x + 1/2,
83/x - 63/x = 1/2,
20/x = 1/2,
x = 40.

LET, X=TOTAL MARKS AND N=NUMBER OF STUDENT.
AS GIVEN INCREASE AVG+1/2 WHEN WRONGLY ADDED.

AVG + 1/2 = X/N.........1

LET CORRECT IT,
AVG = X - 63 + 83/N........2
FROM 1 AND 2.
X/N-1/2 = X/N-20/N,
1/2 = 20/N,
N = 40.

Let x is average marks when total marks are 63.

Let n=total no.of pupils
then, 63/n =x --<1>
83/n = x + 0.5.

From 1, 83/n=63/n+0.5,
20/n = 0.5.
n = 40.

Let x is average marks when total marks are 63.
Replacement,

83 - 63 = 20.
Then, x + 20 = x\2.
X = 40.