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After an old member is replaced by a new member, it is found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the age of the changed member and the new member?

After an old member is replaced by a new member, it is found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the age of the changed member and the new member? Correct Answer 15 years

Calculation: 

Let the ages of the five members at present be a, b, c, d & e years

And the age of the new member be f years. 

So, the new average of five members age = (a + b + c + d + f)/5      ---- (1) 

Now, their corresponding ages 3 years ago = (a-3), (b-3), (c-3), (d-3) and (e-3) years 

So, their average age 3 years ago = (a + b + c + d + e - 15)/5 = x      ----(2) 

a + b + c + d + e = 5x + 15 

a + b + c + d = 5x + 15 - e       ----(3) 

Substituting this value of a + b + c + d = 5x + 15 - e in (1) above, 

The new average = (5x + 15 - e + f)/5 

Equating this to the average age of x years, 3 yrs, ago as in (2) above, 

(5x + 15 - e + f)/5 = x 

(5x + 15 - e + f) = 5x 

Solving, e - f = 15 years

∴The difference of ages between replaced and new member is 15 years.

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