Question

8. The mean weight of 150 students in a class is 60 kg. The mean of boys in the class is 70 kg and that
of girls is 55 kg. Find the number of boys and girls in the class.
(Boys = 50; Girls = 100)
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Answer 1

boys=50

girls=100

Explanation:

1. mean=sum of weight/no. of student
2. no of boys=x
3. no of girls=150-x
4. sum of weight of boys =70*x
5. sum of weight of girls=(150-x)×55
6. mean weight of all student=60(given)
7. (70×x+150-x)55/150
8. 60 solved this equation and find x

Answer 2

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.