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?
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.
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.
Percent population of town = 25000
Growth rate in 23 years = 4% , 5% , 8% respectively
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.
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?
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.
Let the annual rate of growth be R.
(1 + 0.01R)3 = 1.157625
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?
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.
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?
R1 = 10%
R2 = -8%
R3 = 12%
P = Original count of bacteria = 13125000
We know that:
= 13125000 (1.10) (0.92) (1.12)
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?
R1 = 7%
R2 = – 10%
-= 71000 (1.07) (0.9)
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?
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.
Initial investment by Aman = Rs.100000
In first year = loss of 5%
In second year = profit of 10%
In third year = profit of 12 %
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?
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?
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
= 6760000 (1.04)2
Then, Population of the city in 2001 is 7311616.
= 670000 (1.04)-2
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.
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