# The population of a place increased to 54,000 in 2003 at a rate of 5% per annum

(i) find the population in 2001 (ii) what would be its population in 2005?

**Solution:**

(i) Population in the year 2001

Let the population in the year 2001 be 'P' and the population in 2003 is 'A' = 54000

Also, R = 5%, n = 2

A = P[1 + (R/100)]^{n}

54000 = P[1 + (5/100)]^{2}

54000 = P[1 + (1/20)]^{2}

54000 = P × (21/20)^{2}

54000 = P × (21/20) × (21/20)

P = 54000 × (400/441)

P = 48979.6

The population in 2001 = 48980 (approx.)

(ii) Population in the year 2005

Now, the population in 2003 is considered as 'P' = 540000 and the population in 2005 is 'A'

R = 5%, n = 2

A = P[1 + (R/100)]^{n}

A = 54000[1 + (5/100)]^{2}

A = 54000[1 + (1/20)]^{2}

A = 54000 × (21/20)^{2}

A = 54000 × (21/20) × (21/20)

A = 54000 × (441/400)

A = 135 × 441

A = 59535

The population in 2005 = 59535

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 8

**Video Solution:**

## The population of a place increased to 54,000 in 2003 at a rate of 5% per annum (i) find the population in 2001. (ii) what would be its population in 2005?

NCERT Solutions Class 8 Maths Chapter 8 Exercise 8.3 Question 10

**Summary:**

The population of a place increased to 54,000 in 2003 at a rate of 5% per annum (i) The population in 2001 was 48980 (ii) The population in 2005 will be 59535

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