The total population of a town is 50,000. The number of males and females increases by 10% and 15% respectively and consequently the population of the town becomes 56,000. What was the number of males in the town?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 30,000
The population grows by \(56000-50000=6000\). This increase is made up of 10% of the males and 15% of the females.
Assuming the number of males to be \(m\), the females are \(50000-m\):
\(0.10m+0.15(50000-m)=6000\)
\(7500-0.05m=6000\)
\(0.05m=1500\)
\(m=30000\)
Shortcut: If all 50,000 people grew by 15%, the increase would be 7500.
The real increase is 6000, that is, 1500 less
Each male grows 5% less than a female (10% instead of 15%), so 5% of the males is 1500
Males \(=1500\div0.05=30000\)