Question

The population of a particular area 'A' of a city is 5000. It increases by 10% in the first year, decreases by 20% in the second year, and then increases by 30% in the third year. What will be the population of area 'A' at the end of the third year?

• A. 5225
• B. 5720
• C. 4895
• D. 5560

Hint:

Use successive percentage increase and decrease formulas carefully, updating the base population each year.

Answer 1

The Correct Option is B

Step 1: Initial population = 5000
Step 2: Population after 1st year with 10% increase:
\[ 5000 + 10% \text{ of } 5000 = 5000 + 0.10 \times 5000 = 5000 + 500 = 5500 \] Step 3: Population after 2nd year with 20% decrease:
\[ 5500 - 20% \text{ of } 5500 = 5500 - 0.20 \times 5500 = 5500 - 1100 = 4400 \] Step 4: Population after 3rd year with 30% increase:
\[ 4400 + 30% \text{ of } 4400 = 4400 + 0.30 \times 4400 = 4400 + 1320 = 5720 \] Therefore, the population at the end of the third year is 5720.