1. If the population increases by \(r\%\) per year, then after \(n\) years, the population becomes \(P\); \(n\) years ago, the population was \(P\left(1+\cfrac{r}{100}\right)^{-n}\).

2. 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

3. If the population increases by r% every year, and after n years the population becomes p, then what was the population n years ago.

4. 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 ———.

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

6. If the population increases by r% every year and becomes p after n years, then find the population n years ago.

7. 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 \(P\left(1-\frac{r}{100}\right)^n\).

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

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

11. 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 _____.

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

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

14. 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.

15. 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) \(p(1-\cfrac{r}{100})^n\)

16. The population of a state increases by 10% every 3 years. If the current population of the state is 3,993,000, what was the population 6 years ago?

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

18. 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

19. 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

20. The current population of a city is 4,09,600. If the population increases annually at a rate of 6\(\frac{2}{3}\)% , determine the population three years ago.

21. If the value of a machine depreciates by \(r \%\) each year, then after \(n\) years, its value becomes \(V\) rupees. The value of the machine \(n\) years ago was \(V\left(1-\cfrac{r}{100}\right)^{-n}\).

22. If the value of a machine depreciates by \(r \%\) per year, then after \(n\) years, its value becomes \(V\) INR. \(n\) years ago, the value of the machine was \(V\left(1-\cfrac{r}{100}\right)^{n}\).

23. If a machine depreciates by \(r\%\) annually, its value after \(n\) years becomes \(p\) rupees. What was the price of the machine \(n\) years ago?

24. 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 —

25. 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?

26. 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) \(A\left(1+\cfrac{r}{25}\right)^{x}\)