There are 30 boys and 40 girls in a class. if the average age of boys is 10 yrs and average age of girls is 8 yr, then the average age of the whole class is:

The correct option is 8.86 yrs.

Step-by-Step Explanation:

Step 1: Understand the given data

• Number of boys in the class = 30

• Average age of boys = 10 years

• Number of girls in the class = 40

• Average age of girls = 8 years

Step 2: Calculate the total age of all boys

The formula for total value is given by multiplying the average by the count:

$\text{Total Age}=\text{Average Age}\times \text{Number of Students}$

$\text{Total age of boys}=30\times 10=300\text{years}$

Step 3: Calculate the total age of all girls

$\text{Total age of girls}=40\times 8=320\text{years}$

Step 4: Calculate the total age of the whole class

$\text{Total age of class}=300+320=620\text{years}$

Step 5: Calculate the total number of students in the class

$\text{Total students}=30+40=70$

Step 6: Find the average age of the whole class

$\text{Average age of whole class}=\frac{\text{Total age of class}}{\text{Total number of students}}$

$\text{Average age of whole class}=\frac{620}{70}=\frac{62}{7}\approx 8.857\text{yrs}$

Rounding to two decimal places, we get 8.86 yrs.