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4.Average
hard
The average of first three numbers is double of the fourth number. If the average of all the four numbers is $12,$ find the $4^{th}$ number.
A
$16$
B
$\frac{48}{7}$
C
$20$
D
$\frac{18}{7}$
Solution
Let, the numbers be $a, b, c$ and $d,$ respectively.
Now, according to the question,
$\frac{a+b+c}{3}=2 d$
$\Rightarrow a+b+c=6 d$ ….$(1)$
Again, from the question, $\frac{a+b+c+d}{4}=12$
$\Rightarrow a+b+c+d=48$ ….$(2)$
Now, put the value of $a+b+c$ from $(1)$ in $(2),$ we have
$6 d+d=48 \Leftrightarrow 7 d=48$
$\Rightarrow d=\frac{48}{7}$
Standard 13
Quantitative Aptitude