Question

The average weight of three men ${}^{\prime }{X}^{\prime }{,}^{\prime }{Y}^{\prime }$ and ${}^{\prime }{Z}^{\prime }$ is $75$ kgs. Another mand ${}^{\prime }{A}^{\prime }$ joins the group and the average weight now becomes $80kgs$. If another person ${}^{\prime }{B}^{\prime }$ whose weight is $5kgs$ more than ${}^{\prime }A$ replaces ${}^{\prime }{X}^{\prime }$, then the average weight of ${}^{\prime }{Y}^{\prime }{,}^{\prime }{Z}^{\prime }{,}^{\prime }{A}^{\prime }$ and ${}^{\prime }{B}^{\prime }$ will be $85kgs$. What is the weight of ${}^{\prime }{X}^{\prime }$?

• A. $84kgs$
• B. $82kgs$
• C. $78kgs$
• D. $80kgs$

Answer 1

The correct option is D $80kgs$

Here,
Average weight of three men $X,Y$ and $Z=75kgs$.
$\therefore$ Total weight of three men $X,Y$ and $Z=75\times 3=225kgs$.
$A$ joins the group and average weight $=80kgs$
$\therefore$ Total weight of this group $=80\times 4=320kgs$.
$\therefore$ weight of $A=320-225=95kgs$.
$\therefore$ weight of $B$ is $5kg$ more than $A$.
$\therefore$ weight of $B=95+5=100kgs$.
Total weight of $X,Y,A$ and $Z=320kgs$.
Total weight of $X,Y,A,B$ and $Z=320+100=420kgs$.
Total weight of $Y,Z,A$ and $B=85\times 4=340kg$.
$\therefore$ weight of $X=(420-340)=80kgs$.