Question

The mean weight of 150 students in a class is 60kg. The mean of boys in the class is 60kg and that of girls is 55kg. What is the number of boys and girls in the class?

Need the solution within 1 hour. Thanks in advance!

Answer 1

Answer:

Given :-

• The mean weight of 150 students in a class is 60 kg.
• The mean of boys in the class is 60 kg and that of girls is 55 kg.

To Find :-

• What is the number of boys and girls in the class.

Solution :-

Let,

$\mapsto \bf Number\: of\: Boys\: =\: x$

$\mapsto \bf Number\: of\: Girls =\: y$

Now,

★ The mean weight or the total number of students is 150.

So,

$\implies \sf\bold{\purple{x + y =\: 150\: ------\: (Equation\: No\: 1)}}$

Now,

➳ Mean weight of x boys = 60 kg

➙ Total weight of x boys = 60x kg

Again,

➳ Mean weight of y boys = 55 kg

➙ Total weight of y boys = 55y kg

Now,

★ The mean weight of 150 students in a class is 60 kg

So,

➳ Total weight of 150 students = 60 × 150

➙ Total weight of 150 students = 9000 kg

According to the question :

$\implies \sf 60x + 55y =\: 9000$

$\implies \sf\bold{\purple{12x + 11y =\: 1800\: ------\: (Equation\: No\: 2)}}$

Now, by multiplying the equation no 1 by 11 we get,

$\implies \sf x + y =\: 150$

$\implies \sf\bold{\purple{11x + 11y =\: 1650\: ------\: (Equation\: No\: 3)}}$

Again, subtracting equation no 3 from equation no 2 we get,

$\implies \sf 12x + 11y - (11x + 11y) =\: 1800 - 1650$

$\implies \sf 12x {\cancel{+ 11y}} - 11x {\cancel{- 11y}} =\: 150$

$\implies \sf\bold{\red{x =\: 150}}$

By putting x = 150 in the equation no 1 we get,

$\implies \sf x + y =\: 150$

$\implies \sf 150 + y =\: 150$

$\implies \sf y =\: 150 - 150$

$\implies \sf\bold{\red{y =\: 0}}$

[Note : @ProThala I think you have put the question wrong that's why the number of girls is coming 0. Please put the correct question. If you have the correct question you can use my method. ]

Answer 2

let boy be x and girl be y.

mean = sum of weights/ 150

60 × 150 = sum of weight.

sum of weights = 9000.

• The mean of boys in the class is 60kg and that of girls is 55kg.

60x = All boys weight

mean weight of girl = 55kg

no. of girls = Total students - number of boys = 150 - x

Total weight of girls = 55 × ( 150 - x) = 8250 - 55x.

Total weight = Total weight of girls + Total weight of boys

9000 = 60x + 8250 - 55x

9000 - 8250 = 5x

750 = 5x

x = 750/5 = 150

number of boys = 150

x + y = 150

150 + y = 150

y = 0