Aptitude - Average - Discussion

It is actually easy if you get the proper steps, actually I kind of struggled a bit for myself to understand with the limited steps given in answer but I kind of figured out the steps.

Note : I am just an aspiring student and so I don't know if my explanation is correct but its just method I found quite easy to understand

Do it using following steps:

Let the total marks without 1 pupils mark be = y.
Let the total no. of pupil be = x.

It is given that 1 pupil marks entered wrong as 83 and thus increases avg. marks by 1/2.

Therefore,

(y+83)/x = avg.marks + 1/2 -->(i).

But,

The pupil's actual mark is 63.

(y+63)/x = avg.marks --> (ii).

Sub (ii) for avg.marks in (i), then,

(y+83)/x = (y+63)/x +1/2.
=> (y+83)/x - (y+63)/x =1/2.
=> (y + 83 - y - 63)/x = 1/2 [ i have put in brackets to show whole divided by 'x' ].
=> (83- 63)/x =1/2.
=> 20/x = 1/2.
=> x = 40.

Therefore, there are 40 pupils in class.

Let total number be x.
Then it is given that average for 63 is A.
i.e, sum/x = A.

When it is wrongly entered as 83 then.
(sum-63+83) /x = A + 1/2.

Then (sum- 20) /x =A + 1/2.
(sum/x) - (20/x) =A+1/2.

Now pick from above that sum/x=A.
Now A- (20/x) =A + 1/2.

Thus, it brings x=40.

Hi. I have come up with one more simple solution:

1st case:

Lets say avg is X when marks are 63. So X = 63/n.

2nd case:

When marks were noted as 83, the avg is increased by 0.5 so,

X+0.5 = 83/n.

Now if you subtract 2nd case - 1st case then (83-63) /n = X+0.5-X.

So, 20/n = 0.5 and n = 20/0.5 so n = 40.

Have a great day dudes. !

Let the total avg is x and it's given that avg increase by 0.5 then,

x: (3x/2)-83+63

-(x/2): -20

So, x:40 Answer, in question 63 marks are correct so we use +sign and 83 are incorrect so we use -ve sign.

Before..

Av = Sum/num ------(1).

After..

Av+1/2 = (Sum+20)/num -------(2).

Putting value of (1) in (2).

Sum/num + 1/2 = Sum/num + 20/num.

num = 40.

Let total of other students be x and number of students be n,

(x+83)/n - (x+63)/n = 1/2.

(x+83-x-63)/n = 1/2.

20/n = 1/2.

Therefore n = 40.

Hai friends,

Let average marks = x.

Total number of students = n, then
total mark = x*n.

According to the question the difference in the marks is = 83-63 = 20.

x*n/n=x.......(Can you remember that)

Here the difference in the marks is 20 and the average is increased by half so that x+1/2.

So, ((x*n)+20)/n = x+1/2.

Cross multiply we get,

2xn+40 = 2xn+n.

From that we get total number of students,

n=40.

Hi friends.

Let us consider p be the no. of pupil, x be the average.

Case1: original marks 63/p=x ----- average of case 1.
Case2: new marks 83/p=x+1/2 ----average of case 2.

2-1 => (83/p-63/p)=x+1/2-x
=> 20/p=1/2
=> p=40.

Hi guys !

Let no.of people = x (83/x) - (63/x) = 1/2 after solving this we get x= 40 it is very easy method to understand is't it ?

@ sowjanya...

7x/4y +2x/9y=1/1

we get 2:3