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4.Average
hard
Average age of $A, B$ and $C$ is $84\, years.$ When $D$ joins them the average age becomes $80\, years.$ A new person, $E,$ whose age is $4 \,years$ more than $D,$ replaces $A$ and the average of $B, C, D$ and $E$ becomes $78\, years.$ What is the age of $A$ ? (in $years$)
A
$80$
B
$50$
C
$60$
D
$70$
Solution
$\frac{A+B+C}{3}=84$
$A+B+C=84 \times 3=252$ ……$(1)$
Similarly, $\frac{A+B+C+D}{4}=80$
$A+B+C+D=320$ ….$(2)$
So, using $(1) \Rightarrow 252+D=320$
$\therefore D=68(\therefore E=72)$
$\frac{B+C+D+E}{4}=78$
$B+C+D+E=312$
Using $(2) \Rightarrow B+C+68+72=312$
$B+C=172$ …..$(3)$
Put $(3)$ in $(1),$ $\quad A=80$
Standard 13
Quantitative Aptitude
