Village A has a population of 72,000, which is decreasing at the rate of 1,000 per year. Village B has a population of 54,000, which is increasing at the rate of 800 per year. In how many years will the population of both the villages be the same?

Correct option is C

Given:

Village A's initial population: 72,000

Village A's rate of decrease: 1,000 per year

Village B's initial population: 54,000

Village B's rate of increase: 800 per year

Solution:

So, after t years, the population of Village A will be:

Population of A after t years = 72,000−1,000t

So, after t years, the population of Village B will be:

Population of B after t years = 54,000+800t

populations equal to each other:

72,000−1,000t = 54,000+800t

72,000−54,000 = 1,000t+800t

18,000=1,800t

​$$=\frac{18,000}{1,800}$$

t = 10 

So, the populations of both villages will be the same in 10 years.

Thus, correct option is (c)