Question

the average age of all the students of a class is 18 years. the average age of the boys of the class is 20 years and that of the girls is 15 years. if there are 20 girls in the class then find the number of boys in the class? please explain step by step ​

Answer 1

Answer:

The answer is 30

Step-by-step explanation:

Let x be the number of boys in the class,

Also, the average age of the boys = 20, ( given )

Total sum of the ages of boys = 20x

(Since, Sum of the observation = Average × number of the observation )

Now, the number of girls = 20,

And, the average age of the girls = 15

Total sum of the ages of girls = 20 × 15 = 300,

Total students = x + 20

So, the total sum of the ages of the students ( both boys and girls ) = 20x + 300

Average age of class = Total sum of age

Total student

= 20x + 300 = 18

x + 20

20x + 300 = 18 (x + 20)

20x + 300 = 18x + 360

20x - 18x = 360 - 300

2x = 60

x = 30.

x = 30.Hence, There are 30 in the class.

Hope it will help you ☺️.

Answer 2

Answer:

• The number of boys in the class is 30.

Given:

• The average age of all the students of a class is 18 years. The average age of the boys of the class is 20 years and that of the girls is 15 years.

• There are 20 girls in the class.

To find:

• The number of boys in the class.

Solution:

Let the number of boys be x years.

$\boxed{\sf{Average=\dfrac{Sum \ of \ observations}{Number \ of \ observations}}}$

For 20 girls,

Sum of age of 20 girls/20 = 15

=> Sum of age of 20 girls = 15 × 20

=> Sum of age of 20 girls = 300...(1)

For x number of boys,

=> Sum of age of x boys/x = 20

=> Sum of age of x boys = 20x ...(2)

For all the students in the class,

Sum of age of students/Number of students = 18

Here,

Sum of ages of students

= Sum of ages of boys + Sum of ages of girls

i.e. Sum of ages of students = 20x + 300

...from (1) and (2)

Number of students

= Number of boys + Number of girls

i.e. Number of students = x + 20

Therefore, average of students can be given by

=> (20x + 300)/(x + 20) = 18

=> 20x + 300 = 18 (x + 20)

=> 20x + 300 = 18x + 360

=> 20x - 18x = 360 - 300

=> 2x = 60

=> x = 60/2

=> x = 30

Therefore, the number of boys in the class is 30.