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In a class, the number of girls is 33(1/3)% and rest are boys. The average marks of boys in English are 10% less than that of girls and the overall average marks are 84. If average marks of girls in English are G and average marks of boys in English are B, which of the following is/are correct? The Total number of students is 105. I. B + G = 171 II. B – G = 9 III. B × G = (G/10)2 × G                        IV. B : G = 10 : 9

In a class, the number of girls is 33(1/3)% and rest are boys. The average marks of boys in English are 10% less than that of girls and the overall average marks are 84. If average marks of girls in English are G and average marks of boys in English are B, which of the following is/are correct? The Total number of students is 105. I. B + G = 171 II. B – G = 9 III. B × G = (G/10)2 × G                        IV. B : G = 10 : 9 Correct Answer I and III

Given:

Total number of students = 105

Number of girls = 33(1/3)% of 105

Number of boys = 105 – Number of girls

B = 90% of G

Overall average marks in English = 84

Formula Used:

Average = Sum of values/Number of values

Calculation:

Number of girls = 33(1/3) × 105/100

⇒ 1/3 × 105

⇒ 35

Number of boys = 105 – 35

⇒ 70

B = 90% of G

⇒ B = 90/100 × G

⇒ B = (9/10)G

Sum of marks of boys in English/70 = B

⇒ Sum of marks of boys in English = 70B

Sum of marks of girls in English/35 = G

⇒ Sum of marks of girls in English = 35G

Sum of marks in English/105 = 84

⇒ Sum of marks in English = 8820

⇒ 70B + 35G = 8820

⇒ 70 × (9/10)G + 35G = 8820

⇒ 63G + 35G = 8820

⇒ 98G = 8820

⇒ G = 90

B = 9/10 × 90

⇒ B = 81

I. B + G = 171

81 + 90 = 171

⇒ I is correct

II. B – G = 9

81 – 90 = – 9

⇒ II is not correct

III. B × G = (G/10)2 × G           

LHS = 81 × 90

⇒ 92 × 90       

⇒ (90/10)2 × 90         

⇒ (G/10)2 × G = RHS

⇒ III is correct

IV. B : G = 10 : 9

⇒ B : G = 81 : 90 = 9 : 10

⇒ IV is not correct

∴ I and III are correct

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