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.

To find the population of children and adults separately, we can set up a system of linear equations based on the given information.

Step 1: Define the variables
Let the initial number of children in the village be $C$ and the initial number of adults be $A$.

Step 2: Formulate the equations
According to the problem, the total initial population of the village is 11,000. This gives us our first equation:

$C+A=11000$

Next, we are told that the number of children increases by 11% and the number of adults increases by 20%, making the new population 12,660. We can write the expression for the increase in population:
The increase in children is 11% of $C$, which is $0.11C$.
The increase in adults is 20% of $A$, which is $0.20A$.

The total increase in population is the difference between the new population and the initial population:

$12660-11000=1660$

This gives us our second equation:

$0.11C+0.20A=1660$

Step 3: Solve the system of equations
From the first equation, we can express $A$ in terms of $C$:

$A=11000-C$

Now, substitute this expression for $A$ into the second equation:

$0.11C+0.20(11000-C)=1660$

Expand the equation:

$0.11C+2200-0.20C=1660$

Combine the terms containing $C$:

$-0.09C+2200=1660$

Subtract 2200 from both sides of the equation:

$-0.09C=1660-2200$

$-0.09C=-540$

Divide by -0.09 to find $C$:

$C=\frac{-540}{-0.09}$

$C=6000$

Step 4: Find the population of adults
Substitute the value of $C$ back into the expression for $A$:

$A=11000-6000$

$A=5000$

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