Question : The average of the first three numbers is double the fourth number. If the average of all the four numbers is 12. Find the 4th number.
Option 1: $16$
Option 2: $\frac{48}{7}$
Option 3: $20$
Option 4: $\frac{18}{7}$
Correct Answer: $\frac{48}{7}$
Solution :
Let the four numbers be $p, q, r$ and $s$.
$⇒\frac{p+q+ r+s}{4}=12$
$⇒p+q+r+s=48$ ...(i)
$⇒\frac{p+q+r}{3}=2s$
$⇒p+q+r=6s$ ...(ii)
Putting equation (ii) in equation (i), we get,
$⇒6s+s=48$
$⇒7s=48$
$\therefore s=\frac{48}{7}$
Hence, the correct answer is $\frac{48}{7}$.
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