Correct Answer - Option 3 : 35 years
Given∶
After replacing an old member by a new member the average age of the members is the same as it was 5 years ago.
Formula Used∶
Average = Sum of observations / Number of observations
Calculation∶
i) Let the ages of the 7 members at present be a, b, c, d, e, f and g years and the age of the new member be h years
ii) So, the new average age of 7 members = (a + b + c + d + e + f + h) / 7 ----(1)
iii) Their corresponding ages 5 years ago = (a – 5), (b -5), (c- 5), (d – 5), (e -5), (f – 5) and (g -5) years
So, 5 years age let their average ages = [(a + b + c + d + e + f + g)] / 7 = x ----(2)
a + b + c + d + e + f + g = 7x + 35
⇒ a + b + c + d + e + f = 7x + 35 – g (3)
(ii) Put the value of a + b + c + d + e + f from eq. (3) in eq. (1)
The new average age = (7x + 35 – g + h) / 7
Equating this to the average age of 5 years ago in eq. (2)
(7x + 35 – g + h) / 7 = x
⇒ 7x + 35 – g + h = 7x
On solving, we get
g – h = 35
∴ the difference of ages between replaced and new member is 35 years.
