Question

In a class there are 30 girls and 20 boys and their average height is 160 cm. If the average height of girls is 150 cm, then the average height of boys is

• A. 175 cm
• B. 172 cm
• C. 170 cm
• D. 165 cm

Hint:

When group averages are given, convert everything into total sums first.

Answer 1

The Correct Option is A

To determine the average height of the boys, we need to use the concept of weighted averages. This type of problem can be solved by using the formula for the average, which is:

\(\text{Average height} = \frac{\text{Total height of all students}}{\text{Total number of students}}\)

Given:

• Number of girls = 30
• Average height of girls = 150 cm
• Number of boys = 20
• Total number of students = 30 + 20 = 50
• Overall average height = 160 cm

First, calculate the total height of all students, using the overall average:

\(\text{Total height of all students} = 160 \times 50 = 8000 \text{ cm}\)

Next, calculate the total height of the girls:

\(\text{Total height of girls} = 150 \times 30 = 4500 \text{ cm}\)

Now, find the total height of the boys:

\(\text{Total height of boys} = \text{Total height of all students} - \text{Total height of girls}\)

\(\text{Total height of boys} = 8000 - 4500 = 3500 \text{ cm}\)

Finally, calculate the average height of the boys:

\(= \frac{3500}{20} = 175 \text{ cm}\)

Therefore, the average height of the boys is 175 cm. This value aligns with the given option:

• 175 cm - Correct option
• 172 cm
• 170 cm
• 165 cm