The mean weight of 150 students in class is 60 kg. The mean weight of boys is 70 kg and that of girls is 55 kg. What is the number of boys in the class?

Given that total number of students = 150 = ( n₁+ n₂) and
Mean weight of 150 students = 60 kg.
The mean weight of boys a₁= 70 kg and
The mean weight of girls a₂ = 55 kg
Let n₁ and n₂ be the number of boys and girl, respectively.
∴ n₁ + n₂ = 150 ...(i)
11 n₁ + 11 n₂ = 1650 ...(ii)
Average weight = (n₁ a₁ + n₂ a₂) / (n₁ + n₂)
⇒ 60 = (70 n₁ + 55n₂)/150
⇒ 70 n₁ + 55n₂ = 9000
⇒ 14n₁ + 11n₂ =1800 ...(iii)
On subtracting Eq. (ii) from Eq. (iii), we get
3n₁ = 150 ⇒ n₁ = 50
Hence, required number of boys is 50.