Ratio of male to female population of a town in 2010

Solution

Total male population in 2010 = ({13}/{13 + 12} x 25000 = {13/25} x 25000 = 13000) Total female population in 2010 = 25000 − 13000 = 12000 When male population is increased by 20% and female population is decreased by 5%. New male = 1.20 × 13000 = 15600
New female = 0.95 × 12000 = 11400 Total = 15600 + 11400 = 27000 So, A can be the answer. When male population is decreased by 10% and female population is increased by 27.5%. New male = 0.90 × 13000 = 11700
New female = 1.275 × 12000 = 15300 Total = 11700 + 15300 = 27000 So, B can be the answer. When male population is increased by 25% and female population is increased by 10%. New male = 1.25 × 13000 = 16250
New female = 1.10 × 12000 = 13200 Total = 16250 + 13200 = 29450 (≠ 27000) So, C cannot be the answer. Therefore, only A and B can be the answer. Hence, option c.