In the given questions, two quantities are given, one as ‘Quantity I’ and…
2025
In the given questions, two quantities are given, one as ‘Quantity I’ and another as ‘Quantity II’. You have to determine relationship between two quantities and choose the appropriate option.
Quantity I: The average age of 21 people is 64 years. If the age of a new person is added the new average age becomes 64.5 years, then find the age of new person.
Quantity II: There are 14 people in a family and the average age of all the family members is 30 years. A new baby born in a family, after 4 years what will be the average age of all the family members.
- A.
Quantity I > Quantity II
- B.
Quantity I < Quantity II
- C.
Quantity I ≥ Quantity II
- D.
Quantity I ≤ Quantity II
- E.
Quantity I = Quantity II or no relation
Show answer & explanation
Correct answer: A
Concept
Average = (sum of values) / (number of values), so sum = average x count. When a member is added or removed, recompute the total from the new count; and when time passes, every existing member's age rises by that same amount of time.
Quantity I - age of the new person
Total age of the 21 people = 21 x 64 = 1344 years.
After the new person joins there are 22 people with average 64.5, so new total = 22 x 64.5 = 1419 years.
Age of the new person = 1419 - 1344 = 75 years.
Quantity II - average after 4 years
Total age of the 14 members = 14 x 30 = 420 years.
A new baby (age 0) joins, so there are now 15 members and the total is still 420 years.
After 4 years every one of the 15 members is 4 years older, so total = 420 + 15 x 4 = 480 years.
Required average = 480 / 15 = 32 years.
Cross-check and result
Quantity I = 75 years and Quantity II = 32 years. Since 75 > 32, Quantity I is greater than Quantity II.