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 ???


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Answer 1

Answer:

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 :

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

↦

Mean=

TotalNumberofObservations

SumofObservations

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}⟹40=

5

SumofObservations

By doing cross multiplication we get,

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

\implies \sf\bold{\purple{Sum\: of\: Observations =\: 200}}⟹SumofObservations=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⟹5+1

\implies \sf\bold{\green{6}}⟹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}⟶37=

6

(200+y)

By doing cross multiplication we get,

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

\longrightarrow \sf 200 + y =\: 6 \times 37⟶200+y=6×37

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

\longrightarrow \sf y =\: 222 - 200⟶y=222−200

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

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

Answer 2

Answer:

Mean of age of 5 people = 40 years

Mean of age of 5 people = 40 years So total age of persons in room = 40×5 = 200 years

A new person enters the room , let his age be x years

Total persons now in room are 6

New mean age = 37 years

New mean age = 37 years So total age of 6 persons = 37×6 = 222 years

Total age of 6 persons = Total age of 5 persons + x years

222 years = 200 + x years

x years = 222-200 years

x years = 22 years .

Hope it helped you

Thanks !!