Question

The total population of a village is 5000. The number of males and females increases by 10% and 15% respectively and consequently the population of the village becomes 5600. What was the number of males in the village? <br /><br />Pls give a simple explanation which is easy to understand, if possible...????

Answer 1

Let the number of males be x, then number of females will be 5000-x.Now, number of male increases to x + 10% of x = 11x/10Number of females increases to (5000-x) + 15% of (5000 - x) = 5750 - 23x/20
Therefore, total population now is = 11x/10 + 5750 - 23x/20 = 5750 - x/20So, 5750 - x/20 = 5600⇒ x/20 = 150⇒ x = 3000The number of males was 3000.
See what I did was take number of males as x, so obviously number of females is 5000 - x. Now, I increased both by 10% and 15% respectively. Then I added them which is actually equal to 5600. Then, I found out the value of x. Done!

Linear Equation Method:Let the number of males be x and number of females be y.
x + y = 5000   ---- (1)
1.1x + 1.15y = 5600  ---- (2)
Eq (2) - Eq(1) × 1.1, we get
1.1x + 1.15y - 1.1x - 1.1y = 100⇒ 0.05 y = 100⇒ y = 2000.∴ x = 3000.The number of males is 3000.