These problems require more than one step. Choose your own method and show all working clearly.

1. 1. A number is increased by 20%, then the result is increased by 25%. By what single percentage has the original number increased overall?

2. 2. An original price is reduced by 30%, then reduced by a further 20%. What is the equivalent single percentage reduction?

3. 3. A car depreciates by 25% in year 1 and 15% in year 2. Starting at £20,000, find its value after 2 years and calculate the total percentage decrease.

4. 4. A value is increased by 40%. By what percentage must it then be decreased to return to the original value? Give your answer to 1 decimal place.

5. 5. Two shops sell the same television. Shop A sells it for £800 after a 20% reduction. Shop B sells it for £860 after a 25% reduction. Which shop had the higher original price?

6. 6. Alex invests £10,000. For the first 3 years the account pays 4% compound interest per year. For the next 2 years it pays 3% compound interest per year. Find the total amount at the end of 5 years.

7. 7. A population grows at 3% per year. How many complete years does it take for the population to grow by more than 50%?

8. 8. A shop reduces prices by 15%, then increases them by 15%. A customer says prices are back to the original. Show this is incorrect and find the actual percentage difference from the original.

9. 9. Three friends each invest £5,000. Anna receives 5% compound interest per year. Beth receives 4.5% compound interest per year. Carl receives 7% simple interest per year. After 3 years, who has the most money? Show all working.

10. 10. A price is increased by x%, and then the result is decreased by x%. Using algebra, show that the final price is always less than the original, unless x = 0.

11. 11. A house is worth £320,000. It increases by 5% in year 1, decreases by 3% in year 2, and increases by 7% in year 3. Find the value to the nearest pound at the end of year 3.

12. 12. An estate agent charges 1.5% commission on property sales. In one month they sell properties worth £4.8 million in total. How much commission do they earn?

13. 13. A machine produces 2,400 items per day. 2.5% are faulty. After the machine is serviced, the fault rate falls by 40%. How many faulty items are produced per day after the service?

14. 14. An investment grew to £12,597.12 after 3 years at 8% compound interest per year. Find the original amount invested.

15. 15. A school's budget is cut by 12.5%. The head teacher negotiates a restoration of 8% of the new (reduced) budget. What is the overall percentage change from the original budget?

16. 16. A price rises by 20% every year for 3 years. What is the total percentage increase over the 3 years? Explain why this is not the same as three separate 20% increases added together.

17. 17. Maria earns £35,000 per year. She receives a 4% rise in year 1, a 2.5% rise in year 2, and a 3% rise in year 3. Find her salary at the end of year 3.

18. 18. A number is 20% more than a second number. The second number is 25% less than a third number. What percentage of the third number is the first number?

19. 19. A shop owner marks up goods by 40% above cost price, then offers a 10% sale discount on the marked-up price. What is the overall percentage profit on the cost price?

20. 20. Which gives the greater return on a £10,000 investment: 5% compound interest for 10 years, or 6% compound interest for 8 years? Show all working and state the difference.

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