**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, R_{1} = 5.5%

Annual death rate, R_{2} = 3.5%

Net growth rate, R = (R_{1} – R_{2}) = 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,

**4. Three years ago, the population of a town was 50000. If the annual increase during three successive years be at the rate of 4%, 5% and 3% respectively, find the present population.**

**Solution:**

Here,

R_{1} = 4%

R_{2} = 5%

R_{3} = 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:

R_{1} = 10%

R_{2} = -8%

R_{3} = 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:**

R_{1} = 7%

R_{2} = – 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**

**(i) 2001 (ii) 1997**

**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