Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
Three years ago, the average age of a family of six members was 19 years. Since then a boy has been born and the average age of the family is the same today as it was three years ago. What is the age of the boy?
5 years
5 years
2 years
1 year
1 year
Calculate total age increase: 6 members each aged by 3 years contributes 6├Ч3=18 years. The new member is the difference between current sum (7 members ├Ч 19) and previous sum plus aging (6 members ├Ч 19 + 18).
Initial family size = 6, average age 3 years ago = 19, new family size = 7, current average age = 19.
Average=NumberofmembersSumofagesтАЛ
Calculate total age increase: 6 members each aged by 3 years contributes 6├Ч3=18 years. The new member is the difference between current sum (7 members ├Ч 19) and previous sum plus aging (6 members ├Ч 19 + 18).
Students often forget that all 6 original members age by 3 years, adding 18 years to the total sum rather than just 3.
Calculate sum of ages 3 years ago
With 6 members and an average age of 19, the sum of their ages 3 years ago was 6├Ч19=114.
114
Calculate sum of ages today
Each of the 6 original members has aged by 3 years, so the total increase is 6├Ч3=18. Adding this to the previous sum gives 114+18=132.
132
Calculate total sum with the new member
The family now has 7 members with an average age of 19. The total sum is 7├Ч19=133.
133
Find the boy's age
The age of the boy is the difference between the total current sum of 7 members and the current sum of the 6 original members: 133тИТ132=1.
1
D is correct because the boy's age is calculated as the difference between the current total family age of 133 and the sum of the original members' current ages of 132, resulting in 1 year.
This logic is identical to 'replacement' or 'inclusion' problems in mixtures and alligation where adding a component changes the overall mean.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download тАв 100K+ Aspirants