What will be the Difference Between the Age of the New Member? If

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

  1. 2 years
  2. 4 years
  3. 8 years
  4. 15 years
Manish Listener Asked on 15th July 2015 in Maths.
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  • 1 Answer(s)

    Answer: (4). 15 years

    Let the five members of the club be p, q, r, s, and t. a new member be. u.
    and let the average age of member after replacing member be X.
    therefore, the average age of members of the club after an old member replaced by new member = ( p + q + r + s + u ) / 5 = X ……. ( i )

    According to the question, 3 years ago the average is same as average at now.
    3 years ago, the old member present at the club so the corresponding age of members of the club is (p-3) , ( q-3 ), ( r-3 ), ( s-3 ), ( t-3 ).
    and the average of their age =  (p-3) + ( q-3 ) + ( r-3 ) + ( s-3 ) + ( t-3 ) / 5 = X
     = ( p + q + r + s + t – 15 ) = 5X
                                                           = ( p + q + r + s ) = 5X + 15 – s      …………….( ii )

    put the value of ( p + q + r + s + t ) from (ii) to (i) then, we get.
      5X + 15 – s + v = 5x
                                                 u – s = 15
    Hence, the difference between the age of the replace member and the new member is 15 years.

    vijay Professor Answered on 15th July 2015.
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