Question

The population of a city increases at the rate of 5% pa. If the present population of the city is 1,85,220, then what was its population 3 yr ago?
1. 1,81,500
2. 1,83,433
3. 1,60,000
4. 1,27,783

Answer 1

Correct Answer - Option 3 : 1,60,000

Given:

Population increased by 5%

Population of a city = 1,85,220

Formula Used:

Population increase

V_f = V_i (1 + R/100)ⁿ

where,

V_f = Final population

V_ⁱ = initial population

R = Rate 

n = Number of years

Calculation:

Vf = Vi (1 + R/100)n

⇒ 1,85,220 = Vi ×(1 + 5/100)³ 

⇒ 1,85,220 = V_i × (1 + 1/20)³

⇒ 1,85,220 = Vi × (21/20)³

⇒ 1,85,220 = Vi × 21/20 × 21/20 × 21/20

⇒ Vi = (1,85,220 × 20 × 20 × 20)/(21 × 21 × 21)

⇒ Vi = 1,60,000

∴ The population of a city 3 years ago was 1,60,000