The population of a town is 175000. The number of women are 66% of number of men. If the number of men increased by 15%
and the number of women increased by 10%, what is the percentage change in the population of town?
Answers
Answer:
For example
Step-by-step explanation:
GIVEN :
The population of a town = 7500
The number of males increases by 10%
The number of females increases by 25%
After increment in male and female the population of the town = 9000
ASSUMPTION :
Let the male population of the town be x
So, the female population of the town = 7500 – x
CALCULATION :
After increment, the number of male = x × 110/100 = 11x/10
After increment, the number of female = (7500 – x) × 125/100
⇒ 5(7500 – x)/4
⇒ (37500 – 5x)/4
⇒ 11x/10 + (37500 – 5x)/4 = 9000
= (22x + 187500 – 25x)/20 = 9000
⇒ 187500 – 3x = 180000
⇒ 3x = 7500
⇒ x = 2500
∴ The male population of the town is 2500
Alternative Method
Previously population was 7500
Present population 9000
⇒ Overall population increased (90000 - 75000) = 1500
⇒ Overall population increase % = (1500/7500) × 100 = 20%
Male increased by 10% and female increased by 25%
Applying Alligation method get,
Male Female
10% 25%
20%
(25 - 20) = 5% (20 - 10) = 10%
Male : Female = 5 : 10 = 1 : 2
Initially number of male in the town was (1/3) × 7500 = 2500
∴ Number of male in the town was 2500.