The mean weight of 150 students in a certain class is 30 kg. the mean weight of the boys in the class is 40 kg and that of the girls is 25 kg. find the number of boys and girls in the class.
Answers
Answer:
Number of boys=50
Number of girls=100
Step-by-step explanation:
Let be the number of boys= x
∴number of girls=(150-x)
∴According to the given condition,
(x×40)+((150-x)×25) = 150×30
→15x = 150×(30-25)=15×50
→x=50
∴(150-x)=100
MARK ME BRAINLIEST.
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 = 40 kgs
x₂ = Mean weight of girls = 25 kgs
x = Mean weight of all students = 30 kgs
∴ x = (n₁ x₁ + xn₂) / (n₁ + n₂)
⇒ 30 = (n₁ × 40 + n₂ × 25)/ (n₁ + n₂)
⇒ 30 (n₁ + n₂) = 40n₁ + 25n₂
⇒ 30n₁ + 30n₂ = 40n₁ + 25n₂
⇒ 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.