Average of first three numbers is double of fourth number. If average of all four numbers is 12, 4^{

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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

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