Aptitude - Average - Discussion
Discussion Forum : Average - General Questions (Q.No. 15)
15.
A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:
Answer: Option
Explanation:
Let there be x pupils in the class.
| Total increase in marks = |  |
x x | 1 |  |
= | x |
| 2 | 2 |
 |
x | = (83 - 63)  |
x | = 20 x= 40. |
| 2 | 2 |
Discussion:
123 comments Page 10 of 13.
Durga said:
7 years ago
Avg = (sum of observations)/(no. of observations).
Given,
Avg = (x+63)/n ------> (1)
Avg + 1/2 = (x+83)/n ------> (2) (Avg increased by half).
Substituting eqn 1 in eqn 2,
(x+63)/n + 1/2 = (x+83)/n.
(x+83)/n - (x+63)/n = 1/2.
n = 40.
Given,
Avg = (x+63)/n ------> (1)
Avg + 1/2 = (x+83)/n ------> (2) (Avg increased by half).
Substituting eqn 1 in eqn 2,
(x+63)/n + 1/2 = (x+83)/n.
(x+83)/n - (x+63)/n = 1/2.
n = 40.
Yash said:
7 years ago
Thank you @Nik.
Ashok said:
7 years ago
Please explain me, I am not getting this.
Kush said:
7 years ago
I am not getting it. Please someone explain to me briefly.
Bharat Gupta said:
7 years ago
When 63 is entered the let avg is x.
x = (sum of the marks of rest of students+63)/n.
Let the sum of the marks of rest of the students=y.
Therefore, x=(y+63)/n.
When 83 is entered avg is increased by 1/2 or 0.5.
So, x+0.5= (y+83)/n.
Equating both the terms we get;
0.5=20/n.
Therefore, n=40.
x = (sum of the marks of rest of students+63)/n.
Let the sum of the marks of rest of the students=y.
Therefore, x=(y+63)/n.
When 83 is entered avg is increased by 1/2 or 0.5.
So, x+0.5= (y+83)/n.
Equating both the terms we get;
0.5=20/n.
Therefore, n=40.
Arushi Mathur said:
7 years ago
Let x = total no of students, y=Avg of students when 63 is taken.
Sum of students when 63 is taken=xy.
So, (xy-63+83) /x=y+0.5.
(xy-20) =xy-0.5x.
x = 40.
Sum of students when 63 is taken=xy.
So, (xy-63+83) /x=y+0.5.
(xy-20) =xy-0.5x.
x = 40.
Sheik said:
7 years ago
Thanks @Ravi.
Ashwini said:
7 years ago
See the difference 83 and 63, which means extra 20 marks they have given. It increased by 1/2 means we shoud divide 20 by 1/2 which is nothing but 40.
Royal said:
7 years ago
Nice explanation @Nik.
Mudit said:
7 years ago
I didn't understand why we are multiplying x with 1/2? Please tell me.
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