Question

The population of a state is 20000. It increases by 20% during the first year and 30% during the second year. The population after two years will be:

• A. 32000
• B. 40000
• C. 31200
• D. 30000

Hint:

For successive percentage changes, multiply by \((1 + r_1)\) and then \((1 + r_2)\).

Answer 1

The Correct Option is C

To determine the population of the state after two years, let's break down the problem year by year, calculating the population increase accordingly.

1. Initial Population: The starting population is 20,000.
2. First Year Increase: The population increases by 20% in the first year.
   • Calculate 20% of 20,000: \(\text{Increase} = 20,000 \times \frac{20}{100} = 4,000\)
   • Population at the end of the first year: \(20,000 + 4,000 = 24,000\)
3. Second Year Increase: The population increases by 30% in the second year.
   • Calculate 30% of the new population (24,000): \(\text{Increase} = 24,000 \times \frac{30}{100} = 7,200\)
   • Population at the end of the second year: \(24,000 + 7,200 = 31,200\)

Therefore, the population of the state after two years is 31,200.