Village A has a population of 6800, which is decreasing at the rate of 120 per year. Village B has a population of 4200, which is increasing at the rate of 80 per year. In how many years will the population of the two villages will become equal ?

Options

A. a. 9
B. b. 11
C. c. 13
D. d. 16

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the populations after X years
Let the number of years be \( X \).

- The population of Village A after \( X \) years will be:
\[ 6800 - 120X \]
- The population of Village B after \( X \) years will be:
\[ 4200 + 80X \]

### Step 2: Set the populations equal to each other
We want to find out when the populations of the two villages are equal. Therefore, we set the two expressions equal to each other:
\[ 6800 - 120X = 4200 + 80X \]

### Step 3: Rearrange the equation
To solve for \( X \), we first rearrange the equation to get all terms involving \( X \) on one side and constant terms on the other side:
\[ 6800 - 4200 = 80X + 120X \]
This simplifies to:
\[ 2600 = 200X \]

### Step 4: Solve for X
Now, we can solve for \( X \) by dividing both sides by 200:
\[ X = \frac{2600}{200} \]
This simplifies to:
\[ X = 13 \]

### Step 5: Conclusion
Thus, the populations of the two villages will become equal in **13 years**.

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