Multiple choice

In a certain year the percentage of males, females in a village are 45% and 35% respectively and the remaining are children. In the next year the number of males is increased by 100/9%, number of females is increased by 500 and the number of children is increased by 25% due to this change the population of village is increased by 1200. Find the number of females initially present in the village.

  1. 2350

  2. 2230

  3. 2450

  4. 2000
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C Correct answer
Explanation

Let the initial population be P. Then males = 45% of P = 0.45P, females = 35% of P = 0.35P, and children = 20% of P = 0.20P. Male increase = 100/9% of 0.45P = (100/9 × 1/100) × 0.45P = 0.05P. Female increase = 500. Child increase = 25% of 0.20P = 0.05P. Total increase = 0.05P + 500 + 0.05P = 0.10P + 500 = 1200. Solving: 0.10P = 700, so P = 7000. Initial females = 0.35 × 7000 = 2450.

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