Question

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

Answer 1

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.