Multiple choice

In a town, the population of males decreased by $25\%$ from $2001$ to $2002$. The population of females increased by $20\%$ in this period. If females formed $44\dfrac{4}{9}\%$ of the population in $2002$, what percentage of the population in $2001$ were males?

  1. $50\%$
  2. $66\dfrac{2}{3}\%$
  3. $80\%$
  4. $75\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let M and F be male and female populations in 2001. 2002: Males = 0.75M, Females = 1.2F. Females are 4/9 of total: 1.2F / (0.75M + 1.2F) = 4/9. 10.8F = 3M + 4.8F. 6F = 3M, so M = 2F. Total population = 3F. Males were 2F/3F = 2/3 = 66.67%.

AI explanation

Let the male population in 2001 be M and the female population be F, making the male population in 2002 equal to 0.75M and the female population equal to 1.20F. Since females form 44 and 4/9 percent of the population in 2002, we have 1.20F divided by the sum of 0.75M and 1.20F equals 4/9; this simplifies to 0.75M equals 1.50F, or M equals 2F. The required initial percentage of males is M divided by the sum of M and F, which is 2F divided by 3F, and multiplying by 100 gives 66 and 2/3 percent.

Keep practicing — related questions