Shortcut Trick
Applying the continuous percentage growth method:
Final Value = Initial Value × (100 + r1)% × (100 + r2)% × (100 + r3)%
⇒ Present Population = 2,50,000 × (103/100) × (104/100) × (106/100)
⇒ Present Population = (2,50,000 ÷ 10,00,000) × (103 × 104 × 106)
⇒ Present Population = (1/4) × 11,35,472 = 2,83,868
∴ The correct answer is 2,83,868.
Alternate Method
Given:
Initial population (P) 3 years ago = 2,50,000
Successive growth rates for the last 3 years: R1 = 3%, R2 = 4% and R3 = 6%
Formula Used:
Present Population = P × (1 + R1/100) × (1 + R2/100) × (1 + R3/100)
Calculations:
⇒ Present Population = 250000 × (1 + 3/100) × (1 + 4/100) × (1 + 6/100)
⇒ Present Population = 250000 × (103/100) × (104/100) × (106/100)
⇒ Present Population = (250000 ÷ 1000000) × (103 × 104 × 106)
⇒ Present Population = (1/4) × (10712 × 106)
⇒ Present Population = (1/4) × 1135472
⇒ Present Population = 283868
∴ The correct answer is 2,83,868.
Additional Information
Successive Percentage Change
If a value changes by x% and then y%, the net percentage change is given by (x + y + xy/100)%. For three years, this formula can be applied consecutively to find the effective compound rate.
Population Depreciation
If the population of a town decreases by R% annually, the population after n years is given by the formula: A = P × (1 − R/100)n.
Population 'n' Years Ago
If the present population is P and it has been growing at R% annually, the population 'n' years ago can be calculated as: P ÷ (1 + R/100)n.