1. If the population of a village is \(p\) and the annual population growth rate is \(2r\%\), then the population after \(n\) years will be:

(a) \(p(1+\cfrac{r}{100})^n\) (b) \(p(1+\cfrac{r}{50})^n\) (c) \(p(1+\cfrac{r}{100})^{2n}\) (d) \(p(1-\cfrac{r}{100})^n\)

2. If the current population of a village is \(P\) and the annual population growth rate is \(2r\%\), then after \(n\) years the population will be ———.

3. If the population of a village is \(P\) and the annual growth rate of the population is \(2r\%\), then the population after \(n\) years will be ___.

4. If the current population of a village is \(p\) and the annual population growth rate is \(2r\%\), then the population after \(n\) years will be _____.

5. If the population of a village is \(p\) and the annual population growth rate is \(2r\%\), then after \(n\) years, the population will be _____.

6. If the population of a village is \(p\) and the annual population growth rate is \(2r\%\), then the population after \(n\) years will be _____.

7. If the population of a village is \(p\) and the annual growth rate is \(4r\%\), then after \(n\) years the population will be \[ p\left(1+\frac{r}{100}\right)^n \]

8. If the population of a village is \(P\) and the annual population growth rate is \(4r\%\), then after \(n\) years, the population will be \(P\left(1-\cfrac{r}{25}\right)^n\).

9. If the current population of a village is **p**, and the annual growth rate is **2r%**, then after **n years**, the population will be: \[ \text{Population after } n \text{ years} = p \left(1 + \frac{2r}{100} \right)^n \]

(a) \(p\left(1+\cfrac{r}{100}\right)^n\) (b) \(p\left(1+\cfrac{r}{50}\right)^n\) (c) \(p\left(1+\cfrac{r}{100}\right)^{2n}\) (d) \(p\left(1-\cfrac{r}{100}\right)^n\)

10. If the current population of a city is \(P\) and the annual population growth rate is \(r\%\), then after \(n\) years, the population of the city will be \(P\left(1-\frac{r}{100}\right)^n\).

11. If the present population of a village is A and the annual population growth rate is r%, then the population after x years will be –

(a) \(A\left(1+\cfrac{r}{100}\right)^x\) (b) \(A\left(1+\cfrac{r}{50}\right)^x\) (c) \(A\left(1+\cfrac{r}{25}\right)^{2x}\) (d) \(A\left(1+\cfrac{r}{25}\right)^{x}\)

12. If the current population of a village is \(P\) and the annual population growth rate is 20%, then the population 2 years ago was ________.

13. In Pahlampur village, the current population is 10,000. If the population increases annually at a rate of 3%, calculate and write what the population will be after 2 years.

14. The current population of a city is 27,200. If the annual population growth rate is 15%, what will be the population of the city after 2 years?

(a) ₹ 91,972 (b) ₹ 59,972 (c) ₹ 25,972 (d) ₹ 35,972

15. If the current population of a city is 2,66,200 and the annual population growth rate is 10%, then the population 3 years ago was—

(a) 2,00,000 (b) 2,15,000 (c) 2,66,000 (d) none of the above

16. The current population of a city is 25,000. If the annual population growth rate is 10%, what will be the population after 2 years?

(a) 30,250 (b) 25,300 (c) 65,300 (d) none of the above

17. If the population of a village decreases at a rate of 10% per year, then if the current population is 500 people, what will be the population after 2 years?

18. The population of a village increases at a rate of \(\cfrac{x}{2}\)% per year. If the current population is \(xy\), then after \(z\) years, the population will be —

19. In a village, the population increases annually by \(r\%\). If the population after \(n\) years is \(p\), then the population \(n\) years ago was –

(a) \(p\left(1+\cfrac{r}{100}\right)^{-n}\) (b) \(p\left(1-\cfrac{r}{100}\right)^{-n}\) (c) \(p\left(1-\cfrac{r}{100}\right)^n\) (d) None of these

20. The current population of a city is 56,000. If the annual population decline rate is 20%, what will be the population of the city after 2 years?

(a) ₹ 35,000 (b) ₹ 35,840 (c) ₹ 53,840 (d) none of the above

21. If the current population of a city is 28,900 and the annual population decreases at a rate of 15%, then the population 2 years ago was—

(a) 36,900 (b) 40,000 (c) 68,900 (d) 35,700

22. If the current population of a village is \( 2p \) and the population increases by \( 2r\% \) per year, what will be the population after \( 2n \) years?

23. In a certain state, the annual population growth rate is 2%. If the current population is 80,000,000, calculate what the population will be after 3 years.

24. In a village, the current population is \(P\), and it increases by 8% every year. What will the population be after two years?

(a) \((100P+2R)\) (b) \(\frac{(100P+R)(100+R)}{10000}\) (c) \(\frac{(100P+PR)(100+2R)}{10000}\) (d) None of the above

25. The current price of an item is ₹100, and if its price decreases at an annual rate of 10%, then after 2 years the price of the item will be ₹81.

26. The population of a village increases at a rate of 10%. The current population is 5000. In how many years will the population increase to 6050?

27. The population of Maharashtra is \(2\times 10^8\). If the population increases at a rate of 12.5% every two years, what will be the population after 6 years?

28. If the annual compound interest rate is \(r\%\), and the interest earned is _____, then the compound amount of \(p\) rupees in \(n\) years will be \(p\left(1+\cfrac{r}{400}\right)^{4n}\) rupees.

29. The annual population growth rate of a city is 4%. The current population of the city is 196,830. What was the population of the city 3 years ago?

30. The current price of a machine is rupees 2P, and if its price decreases by 2r% each year, then after 2n years, the price of the machine will be:

(a) \(P\left(1-\cfrac{r}{100}\right)^n\) (b) \(2P\left(1-\cfrac{r}{50}\right)^n\) (c) \(P\left(1-\cfrac{r}{50}\right)^{2n}\) (d) \(2P\left(1-\cfrac{r}{50}\right)^{2n}\)