# Exercise 14.4

### 1. The present population of a town is 28000. If it increases at the rate of 5% per annum, what will be its population after 2 years?

#### Solution:

Here,

P = Initial population = 28000

R = Rate of growth of population = 5% per annum

n = Number of years = 2 Hence. The population after two years will be 30870.

### 2. The population of a city is 126000. If the annual birth rate and death rate are 5.5% and 3.5% respectively, calculate the population of city after 3 years.

#### Solution:

Initial population, P = 125000

Annual birth rate, R1 = 5.5%

Annual death rate, R2 = 3.5%

Net growth rate, R = (R1 – R2) = 2%

n = Number of years = 3 Then, the population after three years will be 132651.

### 3. The present population of a town is 25000. It grows at 4%, 5% and 8% during first year, second year and third year respectively. Find its population after 3 years.

#### Solution:

Given,

Percent population of town = 25000

Growth rate in 23 years = 4% , 5% , 8% respectively

Then, #### Solution:

Here,

R1 = 4%

R2 = 5%

R3 = 3%

n =      Number of years = 3 Then, the population after three years will be 56238.

### 5.There is a continuous growth in the population of a village at the rate of 5% per annum. If its present population is 9261, what it was 3 years ago?

#### Solution: Therefore, the population three years ago was 8000.

### 6. In a factory the production of scooters rose to 46305 from 40000 in 3 years. Find the annual rate of growth of the production of scooters.

#### Solution:

Let the annual rate of growth be R. (1 + 0.01R)3  = 1.157625

1+0.01R)3=(1.05)3

1 + 0.01R = 1.05

0.01R = 0.05

R = 5

Then, the annual rate of growth is 5%.

### 7. The annual rate of growth in the population of a certain city is 8%. If its present population is 196830, what it was 3 years ago?

#### Solution: Thus, the population three years ago was 156250.

### 8. The population of a town increases at the rate of 50 per thousand. Its population after 2 years will be 22050. Find its present population.

#### Solution: = 20000

Thus, the population three years ago was 20000.

### 9. The count of bacteria in a culture grows by 10% in the first hour, decreases by 8% in the second hour and again increases by 12% in the third hour. If the count of bacteria in the sample is 13125000, what will be the count of bacteria after 3 hours?

#### Solution:

Given:

R1 = 10%

R2 = -8%

R3 = 12%

P = Original count of bacteria = 13125000

We know that: = 13125000 (1.10) (0.92) (1.12)

= 14,876,400

Then, the bacteria count after three hours will be 14,876,400.

### 10. The population of a certain city was 72000 on the last day of the year 1998. During next year it increased by 7% but due to an epidemic, it decreased by 10% in the following year. What was its population at the end of the year 2000?

#### Solution:

R1 = 7%

R2 = – 10% -= 71000 (1.07) (0.9)

= 69,336

Then, the population at the end of the year 2000 was 69,336.

### 11. 6400 workers were employed to construct a river bridge in four years. At the end of the first-year, 25% workers were retrenched. At the end of the second year, 25% of those working at that time were retrenched. However, to complete the project in time, the number of workers was increased by 25% at the end of the third year. How many workers were working during the fourth year?

#### Solution:

Number of workers = 6,400

At the end of the first year, 25% of the workers were retrenched.

Therefore, 25% of 6,400 = 1,600

Number of workers at the end of the first year = 6,400 – 1600 = 4,800

At the end of the second year, 25% of those working were retrenched.

Therefore, 25% of 4,800 = 1,200

Number of workers at the end of the second year = 4,800 – 1200 = 3,600

At the end of the third year, 25% of those working increased.

Therefore, 25% of 3,600 = 900

Number of workers at the end of the third year = 3,600 + 900 = 4,500

Thus, the number of workers during the fourth year was 4,500.

### 12. Aman started a factory with an initial investment of Rs. 100000. In the first year, he incurred a loss of 5%. However, during the second year, he earned a profit of 10% which in the third year rose to 12%. Calculate his net profit for the entire period of three years.

#### Solution:

Given,

Initial investment by Aman = Rs.100000

In first year = loss of 5%

In second year = profit of 10%

In third year = profit of 12 %

So, Profit = 117040 – 100000= Rs.17040

### 13. The population of a town increases at the rate of 40 per thousand annually. If the present population be 175760, what was the population three years ago?

#### Solution: ### 14.The production of a mixed company in 1996 was 8000 mixies. Due to increase in demand, it increases its production by 15% in the next two years and after two years its demand decreases by 5%. What will be its production after 3 years?

#### Solution: Thus, the production after three years will be 10,051

### 15. The population of a city increases each year by 4% of what it had been at the beginning of each year. If the population in 1999 had been 6760000, find the population of the city in

#### Solution: = 6760000 (1.04)2

= 7311616

Then, Population of the city in 2001 is 7311616.

(ii) = 670000 (1.04)-2

= 6250000

Then, the population of the city in 1997 is 6250000.

### 16. Jitendra set up a factory by investing Rs. 2500000. During the first two successive years his profits were 5% and 10% respectively. If each year the profit was on previous year’s capital, compute his total profit.

#### Solution:

According to question,

Initial investment by jitendra = Rs 2500000

Profit In first 2 successive years = 5% & 10% Then, Hit total profit = 2805000-2500000 = Rs. 387500

Updated: December 3, 2019 — 3:17 pm