# 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

23 views
in Aptitude
closed

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

by (54.0k points)
selected

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.