Aptitude - Average - Discussion

The correct answer is 53.03 not 54.68.

According to me the answer is 53.03.
Because of 50 + 55 + 60 = 165 and not 160,
And 8750/165 = 53.03.

According to me, it is 53.03.

Given;

Student 55 60 45
Average marks 50 55 60
According to formula;- avg=sum/no

Then;

avg = sum of marks(165)/ no of student(3).

Result comes 55.

Given
students 55 60 45.
average marks 50 55 60.

You can take ratios of student in each batch.
i.e. 11 :12 : 9 (55/5:60/5:45/5).

Now solve;
=> 50x11+55x12+60x9 / (11+12+9),
=> 550+660+540/(32),
=> 1750/32,
=> 54.68.

Let T be total marks if all pupil, N be no of students, A be the average mark.
Case 1( when marks were entered correctly ie 63).
T/N=A.
Case 2(83)
(T+20)/N=A+0.5.
Subtract both equations.
20/N = 0.5.
N= 40.

Let assume average as 50. First 55 students.

Here Avg 50 is given. But in case of next 60 members avg 55 given that means 60*5 = 300 extra. In case of remaining 45 students given 60.45*10 = 450 extra.
And totally 300 + 450 = 750 extra.

750 extra on 160 students so 750/160 = 4.68.
And 50 + 4.68 = 54.68 answer.

I am not understanding this, Anyone can explain it?

Let,
1st batch = A , 2nd batch = B , 3rd batch = C, Now,

A/55 = 50 => A= 2750 ( These are the Total marks of each batch of students ).
B/60 = 55 => B= 3300 ( These are the Total marks of each batch of students ).
C/45 = 60 => C= 2700 ( These are the Total marks of each batch of students ).

From above total marks of all batches => A+B+C = 2750+3300+2700 =>8750.

So, Total marks = 8750.
Total number of students in all 3 batches => 55+60+45 =160.

So, now we have to find average of all the students for that we will do,
Total marks / Total number of students = 8750 / 160 => 54.68.

Answer is option (B) = 54.68.

55: 60:45 = 11:12:9.
Choose the origin (assumed average) as 55.
The sum of the deviations = 11x(-5) + 9x5 = -10.
Average = 55 - 10/(11 + 12 + 9) = 55 - 10/32.
You have to subtract about 1/3 which is nearly 0.33. The answer is 54.68.