In a certain year total population of a village was 2000. If the number of men is increased by 10% and that of the woman is decreased by 6%, the total populat

Question

In a certain year total population of a village was 2000. If the number of men is increased by 10% and that of the woman is decreased by 6%, the total population remains unchanged. Previously number of men was?

Answer 1

The starting population was 2000. If we let m be the starting amount of men and w be the starting amount of women, we get this equation:

 

m + w = 2000

 

Now, if the men increase by 10% and the women decrease by 6%, the population stays at 2000.

 

m + .1m + w - .06w = 2000

1.1m + .96w = 2000

 

If we solve for m in the first equation, we get:

 

m = 2000 - w

 

We can use that in the second equation, anywhere there is an m we can substitute 2000-w:

 

1.1(2000-w) + .96w = 2000

2200 - 1.1w + .96w = 2000

-.14w = -200

w = 1428.57

 

We round that to 1429 because when we are talking about a populations, fractions of people don't make sense. If we plug that in to the first equation, we find that there are 571 men in the beginning.