The population of a village is 11000. If the number of children increase by 11% and the number of adults increase by 20%, the population becomes 12660. Find the population of children and adults separately in the village.

The correct option is 6000, 5000.

Let us find the population of children and adults in the village step-by-step.

Let the initial number of children in the village be $C$ and the initial number of adults be $A$.
According to the problem, the total initial population is 11,000. Therefore, we can write our first equation as:
$C+A=11000$
Let this be Equation (1).

Next, we are given that the number of children increases by 11% and the number of adults increases by 20%, making the new total population 12,660.
The new population of children is:
$C+0.11C=1.11C$
The new population of adults is:
$A+0.20A=1.20A$
The sum of these new populations is 12,660. This gives us our second equation:
$1.11C+1.20A=12660$
Let this be Equation (2).

To solve this system of linear equations, we can express $A$ in terms of $C$ using Equation (1):
$A=11000-C$
Now, substitute this expression for $A$ into Equation (2):
$1.11C+1.20(11000-C)=12660$

Expand the equation:
$1.11C+13200-1.20C=12660$
Combine the terms containing $C$:
$-0.09C+13200=12660$
Subtract 13,200 from both sides:
$-0.09C=12660-13200$
$-0.09C=-540$
Divide both sides by -0.09 to solve for $C$:
$C=\frac{-540}{-0.09}$
$C=6000$
Thus, the population of children is 6,000.

Now, find the population of adults by substituting the value of $C$ back into Equation (1):
$A=11000-6000$
$A=5000$
Thus, the population of adults is 5,000.

Therefore, the population of children is 6,000 and the population of adults is 5,000.