LIVE Course for free

Rated by 1 million+ students
Get app now
JEE MAIN 2023
JEE MAIN 2023 TEST SERIES
NEET 2023 TEST SERIES
NEET 2023
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
23 views
in Aptitude by (30.0k points)
closed by

Average score of boys and girls in History are 86 and 91 respectively. The average score of boys and girls in Geography are 88 and 94 respectively. If G is the overall average score in Geography and the overall average score in History is 87 which of the following is/are true?

A. G < 89

B. 88.2 < G < 92.2

C. 86 < G < 91

D. 89 < G < 93


1. B and D
2. Only C
3. A and C
4. B, C, and D

1 Answer

0 votes
by (54.0k points)
selected by
 
Best answer
Correct Answer - Option 4 : B, C, and D

Given:

 

Average score in History

Average score in Geography

Boys

86

88

Girls

91

94

Overall average score

87

G


Formula Used:

Average = Sum of values/Number of values

Calculation:

Let the number of boys is b and the number of girls is g.

Overall average score in History = 87

⇒ (86b + 91g)/(b + g) = 87

⇒ 86b + 91g = (b + g)87

⇒ b = 4g

Overall average score in Geography = (88b + 94g)/(b + g)

Putting b = 4g in above expression

⇒ (88 × 4g + 94g)/(4g + g)

⇒ (352g + 94g)/5g

⇒ 446g/5g

⇒ 89.2

G = 89.2

A. G < 89

89.2 > 89

⇒ A is not true.

B. 88.2 < G < 92.2

88.2 < 89.2 < 92.2

⇒ B is true.

C. 86 < G < 91

86 < 89.2 < 91

⇒ C is true.

D. 89 < G < 93

89 < 89.2 < 93

⇒ D is true

B, C, and D are true.

Short Trick:

Let the number of girls is 1 and the number of boys is b and solve as above.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...