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- Quantitative Aptitude
The average weight of $3 \operatorname{men} A, B$ and $C$ is $84\, kg.$ Another man $D$ joins the group and the average now becomes $80 \,kg .$ If another man $E ,$ whose weight is $3 \,kg$ more than that of $D ,$ replaces $A,$ then the average weight of $B, C, D$ and $E$ becomes $79 \,kg .$ The weight of $A$ is (in $kg$)
$70$
$72$
$75$
$80$
Solution
Average weight of $A, B$ and $C=84 kg$
On joining $D,$ average reduces to $80 kg$.
Let weight of $A , B , C , D$ and $E$ be $a, b, c, d$ and $e$ respectively
$\frac{a+b+c}{3}=84$ …….$(1)$
$\frac{a+b+c+d}{4}=80$ …….$(2)$
$a+b+c=84 \times 3$ …….$(a)$
$a+b+c+d=80 \times 4$ …….$(b)$
(b) $-(a) \Rightarrow d=80 \times 4-84 \times 3$
$=320-252=68$ years
$e=d+3=68+3=71$ years
$\frac{b+c+d+71}{4}=79$ …….$(3)$
$b+c+d+71=79 \times 4$
$b+c+d=79 \times 4-71$
$=245$ …….$(c)$
(b) $-(c) \Rightarrow a=320-245=75$ years
