The population of a city was 120000 in the year 2013. During next year

1.	The population of a city was 120000 in the year 2013. During next year it increased by 6% but due to an epidemic it decreased by 5% in the following year. What was its population in the year 2015?
Answer» Population of a city in 2013, P = 120000 Time, n = 3 years Increasing rate, R = 6% per annum Now, Amount (A) = P (1 + R/100)ⁿ [Where, A = Amount with compound interest P = Present value R = Annual interest rate n = Time in years] ∴Population of the city in the year 2014, ∴ Population = P (1 + R/100)ⁿ = 120000 (1 + 6/100)¹ = 120000 (1 + 3/50) = 120000 (53/50) = 120000 × 53/50 = 2400 × 53 = 127200 ∴ Population of a city in 2014 is 127200. Now, Decreasing rate = 8% ∴ Population of the city in the year 2015, ∴ Population = P (1 - R/100)ⁿ = 127200 (1 - 5/100)¹ = 127200 (1 - 1/20) = 127200 (19/20) = 127200 × 19/20 = 6360 × 19 = 120840 ∴ Population of a city in 2015 is 120840.

The population of a city was 120000 in the year 2013. During next year it increased by 6% but due to an epidemic it decreased by 5% in the following year. What was its population in the year 2015?

Answer»

Population of a city in 2013, P = 120000

Time, n = 3 years

Increasing rate, R = 6% per annum

Now,

Amount (A) = P (1 + R/100)ⁿ [Where, A = Amount with compound interest

P = Present value

R = Annual interest rate

n = Time in years]

∴Population of the city in the year 2014,

∴ Population = P (1 + R/100)ⁿ

= 120000 (1 + 6/100)¹

= 120000 (1 + 3/50)

= 120000 (53/50)

= 120000 × 53/50

= 2400 × 53

= 127200

∴ Population of a city in 2014 is 127200.

Now,

Decreasing rate = 8%

∴ Population of the city in the year 2015,

∴ Population = P (1 - R/100)ⁿ

= 127200 (1 - 5/100)¹

= 127200 (1 - 1/20)

= 127200 (19/20)

= 127200 × 19/20

= 6360 × 19

= 120840

∴ Population of a city in 2015 is 120840.