Say $10600$ is divided into positive quantities $A,B,C,$ and $D$. Use the following information to find the value of $D$: If you remove $A$, the average of the other $3$ numbers is $1000$. If you remove $B$, the average of the other $3$ numbers is $3220$. If you remove $C$, the average of the other $3$ numbers is $3180$.

Given,

$A+B+C+D=10600$ .....$(1)$

If $A$ is removed, average of $B,C,D$ is $1000$.

So,

$B+C+D=3000$

Therefore,

$A=10600-3000=7600$

If $B$ is removed, average of $A,C,D$ is $3220$.

So,

$A+C+D=3220\times 3=9660$

Therefore,

$B=10600-9660=940$

If $C$ is removed, average of $A,B,D$ is $3180$.

So,

$A+B+D=3180\times 3=9540$

Therefore,

$C=10600-9540=1060$

Now,

$D=10600-A-B-C$

$D=10600-7600-940-1060$

$D=1000$