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
The average age of Mohan and his four friends is 36 years. Mohan is 5 years older than the average age of his four friends. Determine MohanтАЩs age in years.
42
40
44
38
40
Total age of 5 people is 5 x 36 = 180 years. If 4 friends have average A, then 4A + (A + 5) = 180, so 5A = 175, A = 35. Mohan is A + 5 = 40 years.
Total age of 5 people is 5 x 36 = 180 years. If 4 friends have average A, then 4A + (A + 5) = 180, so 5A = 175, A = 35. Mohan is A + 5 = 40 years.
Calculate the Total Sum of Ages
There are 5 people in total (Mohan plus his 4 friends). The average age of these 5 people is 36 years. Total Age = 5 x 36 = 180 years.
Set Up Variable for the 4 Friends
Let the average age of the 4 friends be A years. The sum of the ages of the 4 friends is 4 x A = 4A years. According to the question, Mohan's age is 5 years more than the average age of his 4 friends, so Mohan's Age = A + 5.
Formulate and Solve the Equation
Total sum = (Sum of 4 friends) + (Mohan's age) = 4A + (A + 5) = 180. Simplifying gives 5A + 5 = 180, which means 5A = 175, so A = 35.
Find Mohan's Age
Mohan's age = A + 5 = 35 + 5 = 40 years.
A: 42 is incorrect because if Mohan was 42, the 4 friends sum to 138 (average 34.5), but 42 - 34.5 = 7.5!= 5. C: 44 is incorrect because if Mohan was 44, 4 friends sum to 136 (average 34), but 44 - 34 = 10!= 5. D: 38 is incorrect because if Mohan was 38, 4 friends sum to 142 (average 35.5), but 38 - 35.5 = 2.5!= 5.
B is correct because the total sum of ages is 180, and solving 4A + (A + 5) = 180 yields A = 35, making Mohan's age 35 + 5 = 40 years.
In group average problems involving one distinct individual, always represent the distinct individual's value in terms of the group's sub-average to reduce the equation to a single variable.
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