Question

In a group of 71 people, the difference between the age of the eldest and the youngest person is 35 years. when the average age was taken without considering the eldest person the average was reduced by 3% but when the average was taken without considering the youngest person the average was increased by 2%. Find the original average age of all the people. 
1. 12 years
2. 11 years
3. 14 years
4. 10 years

Answer 1

Correct Answer - Option 4 : 10 years

GIVEN:

No of people = 71

Eldest - youngest = 35 years

Change in average without eldest = 3% decrease

Change in average without youngest = 2% increase

FORMULA USED:

Average = sum of all observations/total no of observations

CALCULATION:

Let original average age be x years

Age of eldest person = a years

Age of youngest person = b years 

A.T.Q

97% of x = (71x - a )/70

⇒ 97% of 70x + a = 71x      ----(1)

Also, 102% of x = (71x - b)/70

⇒ 102% of 70x + b = 71x      ----(2)

Equating (1) and (2)

97% of 70x + a = 102% of 70x + b

⇒ 5% of 70x = a - b

∴ 5% of 70x = 35 (a - b = 35)

5/100 × 70x = 35

⇒ x = 10 years

∴ The average age was 10 years