The average age of group of 14 persons is 40 years

The average age of a group of 8 persons is 40 years. A person aged 60 years leaves the group and another person aged 44 years joins the group. The new average age of the group is options: 1.44 years 2

Answer

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The average age of a number of persons in a group was calculated as 35 years, which was 2.5 years more than the correct average as there was an error in recording the age to two persons as 38.5 years and 40 years instead of 29 years and 22 years respectively. The number of persons in the group was:

1. 15
2. 12
3. 11
4. 13

Answer [Detailed Solution Below]

Option 3 : 11

Free

SSC CGL 2021 Tier-I [Held On : 11 April 2022 Shift 1]

100 Questions 200 Marks 60 Mins

Let the number of persons in the group be x, then

Wrong average of age of persons in the group = 35

Wrong sum of age of person in the group = 35x

Correct average of age of persons in the group = 35 – 2.5 = 32.5

Correct sum of age of persons in the group = 32.5x

According to the question

35x – 32.5x = 38.5 + 40 – 29 – 22

⇒ 2.5x = 27.5

⇒ x = 27.5/2.5

⇒ x = 11

Short Trick:

Total number of persons in the group = [38.5 + 40 – 29 – 22]/2.5 = 11

Last updated on Oct 21, 2022

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A group of 15 people has average age of 45 years. Two persons are excluded and the average of the remaining is increased by 5 years. What is the average age of the two persons who have been excluded?

1. 20 years
2. 12.5 years
3. 15 years
4. 10 years 

Answer [Detailed Solution Below]

Option 2 : 12.5 years

Free

10 Questions 10 Marks 7 Mins

Given:

The average age of 15 people = 45 years

After excluding 2 person, average age of remaining = increased by 5 years

Formula Used:

Sum of all numbers = Average of numbers × Number of terms

Calculation:

Total age of 15 people = 45 × 15

⇒ 675 years

Total age of remaining people = [45 + 5] × [15 – 2]

⇒ 50 × 13

⇒ 650 years

Total age of 2 excluded people = Total age of 15 people – Total age of remaining people

⇒ 675 – 650

⇒ 25 years

The average of 2 excluded people = Total age of 2 excluded people/2

⇒ 25/2

⇒ 12.5 years

∴ The average age of the 2 person who have been excluded is 12.5 years.

Latest RRB Group D Updates

Last updated on Sep 27, 2022

The Railway Recruitment Board has released the RRB Group D Answer Key on 14th October 2022. The candidates will be able to raise objections from 15th to 19th October 2022. The exam was conducted from 17th August to 11th October 2022. The RRB [Railway Recruitment Board] is conducting the RRB Group D exam to recruit various posts of Track Maintainer, Helper/Assistant in various technical departments like Electrical, Mechanical, S&T, etc. The selection process for these posts includes 4 phases- Computer Based Test Physical Efficiency Test, Document Verification, and Medical Test. 

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