Find the population of a city after 2 years which is at present 12 lakhs, if the rate of increase is 4% :

Question

Accepted Answer

To find the population of a city after 2 years, given the current population is 12 lakhs and the rate of increase is 4%, we can use the formula for compound interest, which is applicable here as the population grows at a constant percentage rate annually. The formula is:

$$ P = P_0 \times (1 + r)^t $$

Where:
- $ P $ is the future population
- $ P_0 $ is the present population (12 lakhs)
- $ r $ is the rate of increase (4% or 0.04)
- $ t $ is the time in years (2 years)

Substituting the given values into the formula:

$$ P = 12,00,000 \times (1 + 0.04)^2 $$
$$ P = 12,00,000 \times (1.04)^2 $$
$$ P = 12,00,000 \times 1.0816 $$
$$ P = 12,97,920 $$

Thus, the population of the city after 2 years will be 12,97,920, which corresponds to Option 2.

**Explanation for why each option is incorrect:**

1. **Option 1 (12,92,970):** This option is incorrect because it does not accurately reflect the calculation of the population using the compound interest formula. The result of the calculation is 12,97,920, not 12,92,970.

2. **Option 3 (12,02,990):** This option is incorrect as it significantly underestimates the population growth. The calculation clearly shows that the population after 2 years should be much higher than this value.

3. **Option 4 (12,20,990):** This option is incorrect because it also underestimates the population growth. The correct calculation yields a population of 12,97,920, which is much higher than 12,20,990.

In conclusion, Option 2 is the correct answer as it accurately represents the population of the city after 2 years, given the initial population and the rate of increase.