the mean weight of 150 students in a class is 60kg. the mean weight of boys in the class is 70 kg. and that of girls is 55kg . find the number of boys and girls.
Answers
Answer:
Sum of weight/150 = 60
Sum = 9000 kg
Sum of weight(boys)/ x = 70
Sum = 70x
Sum of weight ( girls) / 150-x = 55
Sum = 8250 - 55x
Sum of weight of boys + sum of weight of girls = 9000
70x + 8250 - 55x = 9000
15x = 750
x = 50
No. of boys = 50
No. of girls = 100
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Answer:
Let the number of boys and girls in the class be n₁ and n₂ respectively. Then
n₁ + n₂ = 150 — (i)
We have
x₁ = Mean weight of boy = 70 kgs
x₂ = Mean weight of girls = 55 kgs
x = Mean weight of all students = 60 kgs
∴ x = (n₁ x₁ + xn₂) / (n₁ + n₂)
⇒ 60 = (n₁ × 70 + n₂ × 55)/ (n₁ + n₂)
⇒ 60 (n₁ + n₂) = 70n₁ + 55n₂
⇒ 60n₁ + 60n₂ = 70n₁ + 55n₂
⇒ 10n₁ = 5n₂
⇒ 2n₁ = n₂ — (ii)
• Putting n₂ = 2n₁ from (ii) in (i), we get
⇒ n₁ + 2n₁ = 150
⇒ 3n₁ =150
⇒ n₁ = 50
• Putting n₁ = 50 in n₂ = 2n₁ we get
⇒ n₂ = 100
∴ 50 boys & 100 girls in the class.