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**Hint:**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.

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