
Shortcut Trick
Net percentage change = x + y + (xy/100)
Net change = 5 − 4 + (5 × −4)/100 = 1 − 0.2 = 0.8% increase
Total population at the end of the second year = 100.8%
100.8% = 55,12,248
100% = (55,12,248 ÷ 100.8) × 100 = 54,68,500
∴ The correct answer is 54,68,500.

Alternate Method
Given:
Increase in first year = 5%
Decrease in second year = 4%
Population at the end of the second year = 55,12,248

Let the initial population at the beginning of the first year be P.
⇒ Population after 1st year = P × (1 + 5/100) = P × (21/20)
⇒ Population after 2nd year = [P × (21/20)] × (1 − 4/100)
⇒ 55,12,248 = P × (21/20) × (24/25)
⇒ 55,12,248 = P × (504/500)
⇒ P = (55,12,248 × 500) ÷ 504
⇒ P = 10,937 × 500
⇒ P = 54,68,500
∴ The correct answer is 54,68,500.

Additional Information
Successive Percentage Change
When a value changes by x% and then by y% successively, the effective percentage change is given by (x + y + xy/100)%.
Population Growth Formula
If P is initial population and R1, R2 are growth/decline rates, then Final Population = P × (1 ± R1/100) × (1 ± R2/100).
Ratio Method for Percentage
Convert percentage changes to fractions (e.g., 5% = 1/20) and multiply ratios: (20 → 21) and (25 → 24) to find the total change.