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Common Information

In a Class X Board examination, ten papers are distributed over five Groups – PCB, Mathematics, Social Science, Vernacular and English. Each of the ten papers is evaluated out of 100. The final score of a student is calculated in the following manner.

First, the Group Scores are obtained by averaging marks in the papers within the Group. The final score is the simple average of the Group Scores.

The data for the top ten students are presented below. (Dipan’s score in English Paper II has been intentionally removed in the table).

Note: B or G against the name of a student respectively indicates whether the student is a boy or a girl.

Table below can be scrolled horizontally

 

PCB Group

Math's
Group

Social Science
Group

Vernacular
Group

English
Group

 

Name of the student

Phy.

Chem.

Bio.

 

Hist.

Geo.

Paper I

Paper II

Paper I

Paper II

Final Score

Ayesha(G)

98

96

97

98

95

93

94

96

96

98

96.2

Ram(B)

97

99

95

97

95

96

94

94

96

98

96.1

Dipan(B)

98

98

98

95

96

95

96

94

96

??

96.0

Sagnik(B)

97

98

99

96

96

98

94

97

92

94

95.9

Sanjiv(B)

95

96

97

98

97

96

92

93

95

96

95.7

Shreya(G)

96

89

85

100

97

98

94

95

96

95

95.5

Joseph(B)

90

94

98

100

94

97

90

92

94

95

95.0

Agni(B)

96

99

96

99

95

96

82

93

92

93

94.3

Pritam(B)

98

98

95

98

83

95

90

93

94

94

93.9

Tirna(G)

96

98

79

99

85

94

92

91

87

96

93.7

Q.

Common Information Question: 4/5

Each of the ten students was allowed to improve his/her score in exactly one paper of choice with the objective of maximizing his/her final score. Everyone scored 100 in the paper in which he or she chose to improve.

After that, the topper among the ten students was:

 A.

Ram

 B.

Agni

 C.

Pritam

 D.

Ayesha

 E.

Dipan

 Hide Ans

Solution:
Option(E) is correct

In order to maximize scores, each student would choose to improve his/her score in the paper which would affect the group score the most.

Consider the options.

Ram chooses Vernacular Paper I or II.

His original group score in Vernacular group, $= 94$

His new score would change by:

$\dfrac{\{(94 + 100)/2\} – 94}{5}$ 

$= 0.6$

His new score:

$= 96.1 + 0.6$

$= 96.7$

Agni chooses Vernacular Paper I.

His original group score in Vernacular group $= 87.5$

His new score would change by:

$\dfrac{\{(93 + 100)/2\} − 87.5}{5}$

$= 1.8$

His new score:

$= 94.3 + 1.8$

$= 96.1$

Pritam chooses History.

His original group score in Social Science group, $= 89$

His new score would change by:

$\dfrac{\{(95 + 100)/2\} – 89}{5}$

$= 1.7$

His new score:

$= 93.9 + 1.7$

$= 95.6$

Ayesha chooses Geography.

Her original group score in Social Science group, $= 94$

Her new score would change by:

$\dfrac{\{(95 + 100)/2\} – 94}{5}$

$= 0.7$

Her new score:

$= 96.2 + 0.7$

$= 96.9$

Dipan chooses Mathematics.

His original group score in Mathematics group, $= 95$

His new score would change by:

$\dfrac{100 – 95}{5}$

$= 1$

His new score:

$= 96 + 0.6$

$= 97$,

Which is the highest among the five options.

Hence, option E.


(1) Comment(s)


Kunal
 ()

it is ayesha as she has 96.9 and not dipan who has 96.6