Question
Download Solution PDFThe average age of six members of a family is 40 years. If the age of a guest is included, then the average age increases by 12.5%.What is the age (in years) of the guest?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The average age of 6 members of a family is 40 years.
If the age of a guest is included, then the average age has increased by 12.5%.
Concept used:
Average = Sum of elements/number of elements
Calculation:
Sum of the age of 6 members of a family = 40 × 6
⇒ 240 years
If the age of a guest is included, then the average age has increased by 12.5%,
The average age of 7 persons = 40 × 112.5/100
⇒ 45 years
Sum of the age of 7 persons = 45 × 7
⇒ 315 years
Age of guest = 315 – 240
⇒ 75 years
∴ The age of the guest is 75.
Shortcut Trick
The average age of six members of a family is 40 years,
After the addition of 1 member, the average age increases by 12.5% the average age becomes = 40 × 9/8 = 45 year
The difference of average age is (45 - 40) = 5 year
So, the guest brings (5 × 7) = 35 year age extra
So, the age of the guest is (35 + 40) = 75 year
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