Discussion
The present population of a village is 11,000. If the numbers of males increase by 11% and the numbers of females increase by 20%, then the population will become 12,660. What is the present population of females in the village ?
Answer: C
The present female population is 5,000.
Let the numbers of males and females be M and F. Then \(M + F = 11000\), and after the increases:
\[ \begin{aligned} 1.11M + 1.2F &= 12660 \\ 1.11(11000) + 0.09F &= 12660 \\ 12210 + 0.09F &= 12660 \\ F &= 5000 \end{aligned} \]
Check: 6,000 males rise by 660 and 5,000 females by 1,000, a total rise of 1,660, from 11,000 to 12,660. 6,000 is the number of males, which is the trap.
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