Question

The mean weight of 150 students in a certain class is 60 kg. The mean weight of boys in the class is 70 kg and that of the girls is 55 kgs. Find the number of boys and girls in the class.

A) 100, 50

B) 50, 100

C) 75, 75

D) 60, 90

Answer 1

In this problem; first we will find the total weight of boys and total weight of girls. We are also given a total no of students (boys + girls) as 150. We will use both the relations to find the total number of boys and girls in the class. Apply the formula:

$\text{Mean weight of students}=\dfrac{\text{Total weights of students}}{\text{No of students}}$

Complete step by step solution:

Given: Total no of students in the class = 150

Let number of boys in the class be ‘x’

Let number of girls in the class be ‘y’

∴ x + y = 150 -eq (1) (As it is given that total no of students are 150)

It is also given that, mean weight of boys in the class is 70 kg

i.e. Mean weight of x boys = 70kg

$\text{We know mean weight of boys}=\dfrac{\text{Total weight of all boys}}{\text{Total no of boys}}$

Since, Mean weight of x boys = 70 kg

$\therefore \,\quad \dfrac{\text{Total weight of all }x\text{ boys}}{\text{No of boys}}=70\,\text{kg}$

$\therefore \,\quad \dfrac{\text{Total weight of all boys}}{x}=70\,\text{kg}$

∴ Total weight of x boys = 70 x kg

It is also given that mean weight of y all girls is 55 kgs

i.e. Mean weight of girls = 55 kg

$\dfrac{\text{Total weight of all }y\text{ girls}}{\text{No of girls}}=55\,\text{kg}$

$\dfrac{\text{Total weight of all }y\text{ girls}}{y}=55\,\text{kg}$

∴ Total weight of y girls = 55 y kgs

It is also given that the mean weight of 150 students is 60 kg.

⇒ Mean weight of 150 students = 60 kg

$\Rightarrow \quad \dfrac{\text{Total weight of }150\text{ students}}{\text{No of students}}=60\,\text{kg}$

$\Rightarrow \quad \dfrac{\text{Total weight of }150\text{ students}}{150}=60\,\text{kg}$

∴ Total weight of 150 students = 150 × 60 kg

= 9000 kg

We know,

Total weight of 150 students = Total weight of x boys + Total weight of y girls

= 70x + 55y

∴ 70x + 55y = 9000 -eq (2)

Dividing by 5 on both sides in eq-(2), we get,

14x + 11y = 1800 -eq (3)

We also have x + y = 150

Multiplying 11 on both sides of eq -(1) we get,

11x + 11y = 1650 -eq (4)

Subtracting eq (4) from eq (3), we get:

3x = 150

⇒ x = 50

y = 150 − x = 150 − 50 = 100

y = 100

We got, Total no of boys, x = 50

& Total no of girls, y = 100

∴ Therefore, the correct option is (B). 50,100.

Note: In this question if we knew the formula for average weight, we can solve this question very easily. The formula to calculate the average weight is given by:

$\text{Mean weight of students}=\dfrac{\text{Total weights of students}}{\text{Number of students}}$

You should be very careful in the calculation part as this problem involves a lot of equations.