Question

Five years ago, the average of the ages of 4 persons was 40 years. If a new person joins the group now, then the average of the ages of all five persons is 46 years. The age of the fifth person (in years) is:

• A. 50
• B. 55
• C. 48
• D. 47

Answer 1

Answer:

A. 50

Solution:

Given:

5 years ago,

Average of 4 persons was 40 years.

Now,

Average of 5 persons is 46 years.

Formula Used:

Average = Sum of all observations/Total number of observations

Calclulation:

Five years ago,

The average of 4 persons was 40

⇒ 40 = Sum of ages of 4 persons/4

⇒ Sum of ages of 4 persons $= 40\times{4}$

⇒ Sum of ages of 4 persons = 160 years

Present age = Age of a person 5 years ago + 5 year

⇒ The sum of current ages of all 4 members is,

⇒ $160 +4\times{5}$

⇒ 160 + 20

⇒ 180 years.

Now 5^th member is added and the average is 46 years.

⇒ 46 = Sum of ages of all 5 persons/5

⇒ Sum of ages of all 5 persons $= 46\times{5}$

⇒ Sum of ages of all 5 persons = 230 years.

The age of 5th is,

⇒ 230 – 180

⇒ 50 years

∴ The age of the 5th person is 50 years.