Question

The average age of 50 teachers of a school is 66 years and the average age of 60 teachers of another school is 55 years. What will be average age of teachers of both the schools together?

• A. 60 years
• B. 57.5 years
• C. 65 years
• D. 62.5 years

Answer 1

Answer:

A. 60 years

Solution:

Concept:

In this type of question we have to calculate the total age of each group then add them after that divide the total by total number of members present in the group.

Formula Used:

Average = sum of all the members age in the group / total members in the group

Calculation:

Sum of all the members in the school₁ $= 50\times{66} = 3300$

Sum of all the members in the school₂ $= 60\times{55} = 3300$

Total of both the school = 3300 +3300 = 6600

⇒ Total number of members in the group = 50+60 = 110

⇒ $Average =\frac{6600}{110} = 60$

Shortcut Trick

Teacher in school₁ = 50

Teacher in school₂ = 60

Average age of teacher in school₁ = 66

Average age of teacher in school₂ = 55

Ratio of teacher in school₁ : school₂ = 5 : 6

Let the average age of teacher in both the school together be 60

school1	5	+6
School2	6	-5

 

⇒ $60 + {(5\times{+6}) + (6\times{-5})}$

⇒ 60 + {+30 - 30}

⇒ 60