Question

the population of village is 5000 if in a year no of males were to increase by 5% and that of a female by 3% annually the population would grow to 5202 at end of year find number of males a females

Answer 1

Answer :

Let Total numbers of male = x
And
Number of females = y
So,

x + y = 5000 -------------- ( 1 )

And as males increase by 5 % , So total males = x + $\frac{5x}{100}$ = $\frac{21}{20}$x
And
As females increase by 3 % , So total males = y + $\frac{3x}{100}$ = $\frac{103}{100}$y
So,
We get
$\frac{21}{20}$x + $\frac{103}{100}$y = 5202
Taking LCM we get

105 x + 103y = 520200

105 ( 5000 - y ) + 103y = 520200 ( from equation 1 )

525000 - 105y + 103y = 520200

2y = 525000 - 520200

2y = 4800

y = 2400 substitute that value in equation 1 we get

x + 2400 = 5000

x = 2600

So ,
Total number of males = 2600
And
Total number of females = 2400 ( Ans )