Question

The mean weight of 150 students in a certain class is 60 kilograms. The mean weight of boys in the class is 70 kilograms and that of the girls is 55 kilograms, then the number of boys and girls are

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

Answer 1

The correct option is A $100,50$

Total students in class $=150$

mean weight$=60kg$

total weight $=150\times 60=9000kg$

Let the total number of boys $=x$

mean weight of boys $=70kg$

total weight of boys $=70\times x=70xkg$

total number of girls = total students - no. of boys $=150-x$

mean weight of girls$=55kg$

total weight of girls $=55\times (150-x)=55\times 150-55x=(8250-55x)kg$

Total weight = weight of boys + weight of girls

$9000=70x+(8250-55x)$

$9000=70x+8250-55x$

$9000-8250=70x-55x$

$750=15x$

$x=\frac{750}{15}$

$x=50$

So number of boys $=50$

number of girls $=150-50=100$