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.