The mean age of a class is $16$ years. If the class teacher aged $40$ years old is also included, the mean age increases to $17$ years. The number of students in the class are :

23

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33

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44

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16

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Solution

The correct option is A $23$
Let the number of students $= x$
Mean age $= 16$ years
$∴$ Total age of all students $= 16 x$
New mean age $= 17$ years
$∴$ Total age of all the students $+$ teacher
$= 17 (x + 1)$
Given, $17 (x + 1) - 16 x = 40$
$\Rightarrow x + 17 = 40$
$\Rightarrow x = 23$

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The mean age of a class is 16 years. If the class teacher aged 40 years old is also included, the mean age increases to 17 years. The number of students in the class are :

The correct option is A 23Let the number of students =xMean age =16 years∴ Total age of all students =16xNew mean age =17 years∴ Total age of all the students + teacher=17(x+1)Given, 17(x+1)−16x=40⇒x+17=40⇒x=23

The mean age of a class is $16$ years. If the class teacher aged $40$ years old is also included, the mean age increases to $17$ years. The number of students in the class are :

The correct option is A $23$
Let the number of students $= x$
Mean age $= 16$ years
$∴$ Total age of all students $= 16 x$
New mean age $= 17$ years
$∴$ Total age of all the students $+$ teacher
$= 17 (x + 1)$
Given, $17 (x + 1) - 16 x = 40$
$\Rightarrow x + 17 = 40$
$\Rightarrow x = 23$