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  • The average height of a class of 22 students is 5.8 m and the inclusion of the teacher's height raises the mean by 20 cm. What is the teacher's height?   <p

The average height of a class of 22 students is 5.8 m and the inclusion of the teacher's height raises the mean by 20 cm. What is the teacher's height?

 

 

Option: 1

12.4 m


Option: 2

10.4 m


Option: 3

16.2 m

 


Option: 4

12.4 m


Answers (1)

best_answer

Option (B) 10.4 m

We have to find the height of the teacher, if the average height of a class of 22 students is 5.8 m and the inclusion of the teacher's height raises the mean by 20 cm.

To find the height of the teacher, we can use the formula for the mean:

\mathrm{\text{Mean}=\frac{\text{Sum of student's heights}}{\text{Number of students}}}

The mean height of a class of 22 students is 5.8 m. Therefore,

\mathrm{\frac{\text{Sum of student's heights}}{22}=5.8}

\mathrm{\Rightarrow \text{Sum of student' s heights}=127.6 m}

According to the question,

New mean = 5.8 + 0.2 = 6 m.   [1 m = 100 cm]

Let the height of the teacher be x m. 

So, 

\mathrm{ \frac{127.6+x}{23}=6}

\mathrm{ \Rightarrow 127.6+x=6\times 23}

\mathrm{ \Rightarrow 127.6+x=138}

\mathrm{ \Rightarrow x=138-\ 127.6}

\mathrm{ \Rightarrow x=\ 10.4 m}

Thus, the height of the teacher is 10.4 m.

Posted by

Nehul

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