Question

The mean age of 5 people in a room is 40 years.
A person enters the room.
The mean age is now 37.
What is the age of the person who entered the room?

Answer 1

Mean = sum/number of observations.

Mean age of 5 people:

40 = (sum of ages of 5 people)/5

200 = sum of ages of 5 people

Let the age of new man be 'x'. Now,

Sum of ages = 200 + x

Number of ages(people) = 5 + 1 = 6

Mean = 37

=> (200 + x)/6 = 37

=> 200 + x = 222

=> x = 222 - 200

=> x = 22

Age of the person who entered the room is 22 year.

Answer 2

Answer:

Given :-

• The mean age of 5 people in a room is 40 years. A person enters the room. The mean age is now 37.

To Find :-

• What is the age of the person who entered the room.

Formula Used :-

$\clubsuit$ Mean Formula :

$\mapsto\: \sf\boxed{\bold{\pink{Mean =\: \dfrac{Sum\: of\: Observations}{Total\: Number\: of\: Observations}}}}$

Solution :-

First, we have to find the sum of observations age of 5 people in a room :

Given :

• Mean = 40
• Number of Observations = 5

According to the question by using the formula we,

$\implies \sf 40 =\: \dfrac{Sum\: of\: Observations}{5}$

By doing cross multiplication we get,

$\implies \sf Sum\: of\: Observations =\: 5(40)$

$\implies \sf\bold{\purple{Sum\: of\: Observations =\: 200}}$

Now, we have to find the value of the age of the person who entered the room :

Let,

$\mapsto$ The age of people entered the room be y

Then,

$\leadsto$ Sum of Observations = 200 + y

$\leadsto$ Number of Observations of age of people :

$\implies \sf 5 + 1$

$\implies \sf\bold{\green{6}}$

$\leadsto$ Mean = 37

Given :

• Mean = 37
• Sum of Observations = 200 + y
• Total Number of Observations = 6

According to the question by using the formula we get,

$\longrightarrow \sf 37 =\: \dfrac{(200 + y)}{6}$

By doing cross multiplication we get,

$\longrightarrow \sf 200 + y =\: 6(37)$

$\longrightarrow \sf 200 + y =\: 6 \times 37$

$\longrightarrow \sf 200 + y =\: 222$

$\longrightarrow \sf y =\: 222 - 200$

$\longrightarrow \sf\bold{\red{y =\: 22}}$

$\therefore$ The age of people entered the room is 22 year.