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Question

# The Population of one town is 43,425. About 125 people move out of the town each month. Each month 200 people on average move into town. A nearby town has a population of 45000. It has no one moving in and an average of 150 people moving away every month. In about how many months will the population of the towns be equal ?

Hint:

### ○ Form the equation according to given information..

○ Take variable values as x or any alphabet.

○ Solve the equation to get value of x.

○ Add no. of people coming in and subtract no. of people going out to get net population of town.

## The correct answer is: ⇒ x = 7

### ○ Given:

Town 1: Population 43,425

in 200 people and out 125 people.

Town 2: Population 45,000

out 150 people.

○ Step 1:

○ Let the number of months after which population be equal be x months.

First consider case of Town 1:

As, number of people coming in is more than going out, so population will increase,

Hence, population of Town 1 at the end of month will be =

43,425 + 200 - 125

And after end of x months =

43,425 + (200 -125)x = 43,425 + 75x

Now, consider case of Town 2:

As, 150 people move out every month.

Hence, population of Town 2 at the end of month will be =

45,000 - 150

And after end of x months =

45,000 - 150x

○ Step 2:

○ Now equate the population of both town:

43,425 + 75x = 45,000 - 150x

75x + 150x = 45,000 - 43,425

225x = 1,575

x =

x = 7

- Final Answer:

Hence, after 7 months population of both town will be equal.

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