1. In your uncle's factory, the value of a machine depreciates at a rate of 10% per year. If the current value of the machine is ₹6000, what will its value be after 3 years?

2. The price of a machine in a factory is ₹1,80,000. The value of the machine depreciates by 10% every year. What will be the value of the machine after 3 years?

3. If the price of a washing machine is ₹12,000 and the annual appreciation rate is 10%, what will be its price after 3 years?

(a) ₹ 14,972 (b) ₹ 15,972 (c) ₹ 12,152 (d) ₹ 12,972

4. The value of a machine in my uncle’s factory depreciates at the rate of 10% per year. If the current value of the machine is ₹60,000, let’s determine what its value will be after 3 years.

5. In a local lathe workshop, the value of a machine depreciates by 10% each year. If the current value of the machine is ₹100000, calculate and write what its value will be after 3 years.

6. 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

7. The current price of a machine is \( 2p \) rupees, and its value decreases by \( 2r\% \) annually. After \( 2n \) years, the price of the machine will be \( 2p\left(1 - \cfrac{2r}{100}\right)^{2n} \) rupees.

8. The value of a machine in a factory is ₹180000. The machine’s value depreciates by 10% every year. Calculate what the value of the machine will be after 3 years.

9. The value of a machine used in a factory depreciates at a rate of 10% per year. If the value of the machine after 3 years is ₹43,740, what is its present value?

10. If the current price of a machine is ₹\(b\) and its value depreciates by \(r\%\) every year, then after \(n\) years, the value of the machine will be ₹\(b\left(1 - \cfrac{r}{100}\right)^n\).

11. 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

12. 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

13. If the ratio of the principal amount to its increased value after one year is 25:27, then what will be the annual interest rate?

(a) 2% (b) 4% (c) 6% (d) 8%

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 current price of a machine is ₹2p and its value decreases by 2r% each year, then after 2n years the price of the machine will be:

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

16. A tree's height increases at a rate of 20% per year. If the current height of the tree is 20 meters, what will its height be after 2 years?

17. If interest is compounded every 6 months, then at an annual compound interest rate of 10%, what will be the compound amount and compound interest on ₹8000 for 1½ years?

18. 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.

19. The price of a mobile phone decreases by 5% annually. If its current price is ₹16,400, what will be its price after 2 years?

(a) ₹ 15,801 (b) ₹ 14,801 (c) ₹ 13,401 (d) ₹ 12,801

20. 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?

21. 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) \(2P\left(1-\cfrac{r}{50}\right)^{2n}\)

22. At an annual simple interest rate of 12%, if the ratio of principal to interest after \(x\) years is 25:24, what is the value of \(x\)?

(a) 8 (b) 10 (c) 12 (d) 5

23. If one root of the quadratic equation \(3x^2 + (k - 1)x + 9 = 0\) is 3, then what will be the value of \(k\)?

(a) -11 (b) 11 (c) 12 (d) 14

24. ₹1200 is lent at an annual interest rate of 6\(\frac{1}{4}\)% and ₹1000 is lent at an annual interest rate of 4\(\frac{1}{3}\)% on the same day. After how much time will the amounts (principal + interest) of both loans become equal?

(a) 20 years (b) 24 years (c) 15 years (d) 30 years

25. A person weighs 80 kg. To lose weight, he started going for regular morning walks. He decided that at the beginning of each year, he would reduce his weight by 5% of whatever it was at that time. What will his weight be after 3 years?

26. A farmer deposited some money in the village post office. After 4 years, he found that the total amount including interest had become ₹434. He calculated that the interest he received was \(\frac{6}{25}\) of his principal amount. Find how much money he had originally deposited and what annual rate of simple interest the post office gave.

27. At an annual interest rate of 4%, what will be the total amount (including interest) on ₹450 after 3 years?

(a) ₹ 135 (b) ₹ 180 (c) ₹ 504 (d) ₹ 6000

28. 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 ———.

29. Mr. Amal bequeaths ₹56,000 in his will for his two sons aged 13 and 15 in such a way that, when they each turn 18, the simple interest earned at an annual rate of 10% will be equal to the principal for each. What will be the allocated amount for each son in the will?

30. At an annual simple interest rate of \(\cfrac{a}{5}\)%, if the interest on ₹\(a^2\) for \(\cfrac{a}{3}\) years equals the principal amount, then what is the value of \(\cfrac{a^3}{60}\)?