Question : The average age of six members of a family is 40 years. If the age of a guest is included, then the average age is increased by 12.5%. What is the age (in years) of the guest?
Option 1: 59
Option 2: 65
Option 3: 75
Option 4: 69
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Correct Answer: 75
Solution :
The sum of the age of 6 members of a family = $40 \times 6$ = 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 = $40 \times\frac{112.5}{100}$ = 45 years
The sum of the age of 7 persons = $45 \times 7$ = 315 years
Age of guest = 315 – 240 = 75 years
Hence, the correct answer is 75.
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