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During the first year the population of a village is increased by 5% and the second year it is diminished by 5%. At the end of the second year its population was 31500. What was the population at the beginning of the first year?
  • a)
    35500
  • b)
    31578
  • c)
    33500
  • d)
    33000
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
During the first year the population of a village is increased by 5% a...
x * 105/100 * 95/100 = 31500
x = 31500 * 100/105 * 100/95
D = 31578
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Most Upvoted Answer
During the first year the population of a village is increased by 5% a...
x * 105/100 * 95/100 = 31500
x = 31500 * 100/105 * 100/95
D = 31578
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Community Answer
During the first year the population of a village is increased by 5% a...
Problem: Find the population of the village at the beginning of the first year if the population has increased by 5% in the first year and decreased by 5% in the second year, and the population at the end of the second year is 31500.

Solution:

Let the population at the beginning of the first year be x.

In the first year, the population increased by 5%, so the population at the end of the first year was:

x + 5% of x = x + 0.05x = 1.05x

In the second year, the population decreased by 5%, so the population at the end of the second year was:

1.05x - 5% of 1.05x = 1.05x - 0.0525x = 0.9975x

It is given that the population at the end of the second year was 31500. Therefore:

0.9975x = 31500

x = 31578.95

Therefore, the population at the beginning of the first year was 31578.95, which is approximately equal to 31578.

Answer: Option B (31578)
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