Average age of A, B and C is 84, years. When D joins them average age becomes 80, years. A new perso

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4.Average

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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

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