Answer
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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:
Complete step by step solution:
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:
$\text{Mean weight of students}=\dfrac{\text{Total weights of students}}{\text{No of students}}$
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.
$\text{Mean weight of students}=\dfrac{\text{Total weights of students}}{\text{Number of students}}$
You should be very careful in the calculation part as this problem involves a lot of equations.
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