Question

2 years ago the mean age of 40 people was 11 years. Now a person left the group and the mean age is changed to 12 years. Find the age of the person who left the group.

Answer 1

Given :

Statement 1 :

Two years ago the mean age of 40 people was 11 years .

⇒ So, at present the mean age will be increased by 2,.

Hence, the mean age at present will be 11 + 2 = 13 years,.

Statement 2 :

now a person left the group and the mean age is changed to 12 years,.

⇒ So, the number of people reduced by 1 & the mean changes to 12 years,.

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We know that,

Mean = \frac{Sum (of) (all) (the) (obeservations)}{total(number)(of)(observations}total(number)(of)(observationsSum(of)(all)(the)(obeservations)​ 

⇒ \frac{Sum (of) (all) (the) (obeservations)}{40} = 1340Sum(of)(all)(the)(obeservations)​=13 

⇒ Sum of all the observations = 40 x 13

⇒ Sum of all the observations = 520

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Let the age of the man be x,

Then,

after he left the group,

⇒ \frac{520-x}{40-1} = 1240−1520−x​=12 

⇒ 39 x 12 = (520 -x)

⇒ 468 = 520 - x

⇒ x = 520 - 468

⇒ x = 52

   ∴ The age of the person who left the group is 52 years

Answer 2

The average age of a group of 5 members is 20 years --> the sum of the ages is 5*20=100;
Two years later the sum of the ages of these 5 members would be 100+5*2=110;

Now, say the age of the new member is x years, so the sum of the ages of a new 6 member group is 110+x. Since given that the average age of this group of 6 members is 22 years then: 22*6=110+x --> x=22.

Answer: C.
*said me as brainiest*