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 girls if $55$kg, then number of boys and girls respectively are

• A. $100,50$
• B. $50,100$
• C. $75,75$
• D. $60,90$

Answer 1

The correct option is B $50,100$

Let the number of boys be denoted by $b$ and number of girls be denoted by $g$

We know that,

Sum of all observations = Mean of observations $\times$ No. of observations.

Therefore,

Sum of weight of boys $=70b$ and

Sum of weight of girls $=55g$

Total weight of all students $=60\times 150$

Therefore,

$(b\times 70)+(g\times 55)=(b+g)60$

$\Rightarrow 70b+55g=150\times 60$

$\Rightarrow 70b+55g=9000$ ...(i)

Also. $b+g=150$ or $b=150-g$...(ii)

Solving $\left(1\right)$ and $\left(2\right)$, we get,

$\Rightarrow 70(150-g)+55g=9000$

$\Rightarrow 10500-70g+55g=9000$

$\Rightarrow 1500=15g$

$\therefore g=100$

Hence, $b=150-100=50$