Question

population of a village is 8000 . if 6%men and 10% women are added the population becomes 8600 then the number of men in the village is ?

Answer 1

 X = number of females now 
8000 - X = number of males now 

The increased number of males + the increased number of females equals the new population 

1.06*(8000 - X) + 1.1*X = 8600 

simplify and solve for X 

8480 - 1.06X + 1.1X = 8600 

8480 - 8480 + 0.04X = 8600 - 8480 

0.04X = 120 

divide both sides by .04 

.04X / .04 = 120 / .04 

X = 3000 

Answer 2

Let number of men in a village be x and number of women be y.

Then, according to question,

x + y = 8000                         ....(1)

and 6% of x + 10% of y = 8600 - 8000

i.e 6x + 10y = 60000

=> 3x + 5y = 30000             ....(2)

Solving equations (1) and (2) , we get

y = 3000 and x = 5000

Therefore, initially population of men was 5000.

Current population of men = 5000 + 6% of 5000

= 5000 + 300

= 5300