After replacing an old member with a new memb | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the sum of the ages of the $5$ members $3 \, 	ext{years}$ ago be $S$.Then,the average age $3 \, 	ext{years}$ ago was $\frac{S}{5}$.The curre

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(D) Let the sum of the ages of the $5$ members $3 \, 	ext{years}$ ago be $S$.Then,the average age $3 \, 	ext{years}$ ago was $\frac{S}{5}$.The current sum of the ages of the same $5$ members (without replacement) would be $S + (5 	imes 3) = S + 15$.Let the age of the old member be $X$ and the new member be $Y$.After replacing the old member with the new member,the new sum of ages is $(S + 15) - X + Y$.The new average age is $\frac{S + 15 - X + Y}{5}$.According to the problem,this new average is equal to the average age $3 \, 	ext{years}$ ago,which is $\frac{S}{5}$.So,$\frac{S + 15 - X + Y}{5} = \frac{S}{5}$.$S + 15 - X + Y = S$.$15 - X + Y = 0$.$X - Y = 15$.Therefore,the difference between the ages of the replaced member and the new member is $15 \, 	ext{years}$.

After replacing an old member with a new member,it was found that the average age of five members of a club is the same as it was $3 \, \text{years}$ ago. What is the difference between the ages of the replaced member and the new member (in $\text{years}$)?

Similar Questions

$A$ number,$x$,equals $80 \%$ of the average of $5, 7, 14$ and a number $y$. If the average of $x$ and $y$ is $26$,then the value of $y$ is:

The average of five numbers is $6.9$. If one of the numbers is deleted,the average of the remaining numbers is $4.4$. What is the value of the number deleted?

Five years ago,the average age of a husband and wife was $23 \text{ years}$. Today,the average age of the husband,wife,and child is $20 \text{ years}$. How old is the child in years?

$3 \, \text{years}$ ago,the average age of a family of $5 \, \text{members}$ was $17 \, \text{years}$. With the birth of a new baby,the average age of the $6 \, \text{members}$ remains the same even today. Find the age of the new baby in years.

The average age of a group of $15$ students is $10 \, \text{years}$. When $5$ more students joined the group,the average age increased by $1 \, \text{year}$. If the average age of the $5$ new students is $x$,find the value of $x$ (in $\text{years}$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module