The problem in the image states:

The present population of a city is 20,000. The population increases by 10% in the first year and decreases by 10% in the second year. How will you find the population of the city after two years?

Solution:

We need to account for the percentage increase and decrease in the population in consecutive years. Let's calculate step by step.

Step 1: Population after the first year

An increase of 10% means the population after the first year becomes: $\text{Population after 1 year} = 20000 + (10\% \text{ of } 20000)$ $\text{Population after 1 year} = 20000 \times 1.10 = 22000$

Step 2: Population after the second year

A decrease of 10% means the population after the second year becomes: $\text{Population after 2 years} = 22000 - (10\% \text{ of } 22000)$ $\text{Population after 2 years} = 22000 \times 0.90 = 19800$

Final Answer:

The population of the city after two years will be 19,800.

Would you like a deeper explanation or have any further questions?

Expanding Questions:

1. What formula can be used for successive percentage changes?
2. How do we calculate net population change over two years as a single percentage?
3. What happens if the population increases by 20% in the first year instead of 10%?
4. Can you derive a general formula for cases with "n" years of percentage changes?
5. What is the difference between successive percentage change and direct percentage addition?

Tip:

When dealing with successive percentage changes, always calculate them step-by-step, as percentages are applied to the changing base value.