Percentages and ratio · Ages 12–13

One change after another worksheet

Part of: Percentages (I)

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Percentages and ratio · Ages 12–13

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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.500 goes up 50%, then up 20% more: the result =
Answer:
2.300 goes up 40% to , then down 25% to .
Fill in each blank
Answer:
3.400 goes up 10%, then up 10% more: the result =
Answer:
4.350 goes up 10% to , then down 40% to .
Fill in each blank
Answer:
5.A number goes up 30%, then down 20%. It ends at % of where it started
Answer:
6.A machine worth $34,000 loses 15% of its value each year. What is it worth after two years?
Answer:

7.A $1,000 item goes up 30%, then down 30%. How does its price now compare with before?
- A. 30% lower
- B. 9% lower
- C. The same
- D. 9% higher
Choose the right answer
Answer:
8.A $200 item goes up 40%, then down 40%. How does its price now compare with before?
- A. 16% higher
- B. 40% lower
- C. 16% lower
- D. The same
Choose the right answer
Answer:
9.A number goes up 25%, then down 20%, and ends where it started.
True or false?
Answer:
10.A town of 20000 people grows 5% a year. By what percentage has it grown after two years?
- A. 5%
- B. 10.25%
- C. 25%
- D. 10%
Choose the right answer
Answer:
11.A town of 2000 people grows 5% a year. By what percentage has it grown after two years?
- A. 10%
- B. 5%
- C. 25%
- D. 10.25%
Choose the right answer
Answer:
12.Ka-yee has saved 150% more than Ka-lok. By what percentage is Ka-lok's saving less than Ka-yee's?
- A. 150%
- B. 60%
- C. 40%
- D. 250%
Choose the right answer
Answer:

13.A town has 664 thousand people and is expected to grow 20% a year. How many thousand people after two years?
Working:
Answer:
14.Ka-lok has 25% more stamps than Ka-yan, and they have 225 together. How many does Ka-lok have?
Working:
Answer:
15.An item is cut 40%, then raised 30%. It now costs more than at first.
True or false?
Working:
Answer:
16.A club's fee rose 25%, then 4% the next year, to $2,548. What was the fee at first?
Working:
Answer:
17.A computer is worth $13,000. It loses 20% the first year and 20% the second. After one year it is worth $, after two $, and it has lost % in all.
Fill in each blank
Working:
Answer:
18.A new car is worth $360,000 and loses 50% of its value each year. What is it worth after 3 years?
Working:
Answer:

Show the answers and working

One change after another worksheet: Answers and working

1. 900
After the first it is 750; the second takes 750 as its base, not 500: 750 × (1 + 20%) = 900.
2. 420, 315
300 × (1 + 40%) = 420, and 420 × (1 − 25%) = 315. The 25% decrease is of 420.
3. 484
After the first it is 440; the second takes 440 as its base, not 400: 440 × (1 + 10%) = 484.
4. 385, 231
350 × (1 + 10%) = 385, and 385 × (1 − 40%) = 231. The 40% decrease is of 385.
5. 104
Multiply: 1.3 × 0.8 = 1.04, that is 104%. Or start from 100 and go step by step.
6. 24,565 dollars
Each year leaves 0.85 of it: 34000 × 0.85 × 0.85 = 24565. The second year's loss is of 28900, not of 34000.

7. B. 9% lower
1000 × 1.3 × 0.7 = 910, 90 below the old price, so 9% lower.
8. C. 16% lower
200 × 1.4 × 0.6 = 168, 32 below the old price, so 16% lower.
9. True
1.25 × 0.8 = 1. Only a result of 1 brings it back to the start.
10. B. 10.25%
20000 × 1.05 × 1.05 = 22050, which is 1.05 × 1.05 times as many: 10.25% more.
11. D. 10.25%
2000 × 1.05 × 1.05 = 2205, which is 1.05 × 1.05 times as many: 10.25% more.
12. B. 60%
Say Ka-lok has 100; then Ka-yee has 250. Ka-lok has 150 less, and 150 ÷ 250 × 100% = 60%.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 956.16 thousand
664 × 1.2 × 1.2 = 956.16. The second year grows from the first year's figure.
14. 125 stamps
Ka-yan is the base: Ka-yan has x and Ka-lok x × (1 + 25%), 225 together, so x = 100 and Ka-lok has 125. Not 25% of 225.
15. False
(1 − 40%) × (1 + 30%) leaves 78% of the old price. Only above 100% is it dearer.
16. 1,960 dollars
x × 1.25 × 1.04 = 2548; undo it: 2548 ÷ 1.04 = 2450, 2450 ÷ 1.25 = 1960.
17. 10,400, 8,320, 36
13000 × (1 − 20%) = 10400, 10400 × (1 − 20%) = 8320; it keeps 8320 ÷ 13000 of its value, a 36% loss in all, less than 20% + 20%.
18. 45,000 dollars
Each year leaves 0.5, three times over: 360000 × 0.5 × 0.5 × 0.5 = 45000. Not 3 × 50% off at once.

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