# 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

- 2 years
- 4 years
- 8 years
- 15 years

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.**