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In a club of 7 members, it was found that after replacing an old member by a new member the average age of the members is the same as it was 5 years ago. What is the between ages of the replaced and the new member?
1. 37 years
2. 45 years
3. 35 years
4. 47 years

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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.

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