Percentages and ratio · Ages 13–14

Changes in the parts worksheet

Part of: Percentages (II)

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Percentages and ratio · Ages 13–14

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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.The price rises 20% and the number sold rises 20%: the takings rise %
Answer:
2.A triangle's base grows 20% and its height shrinks 10%: its area becomes times as much, % more.
Fill in each blank
Answer:
3.The price rises 20% and the number sold rises 10%: the takings rise %
Answer:
4.A cuboid's length, width and height all grow 10%: its volume grows %
Answer:
5.A club has 900 men and 300 women. This year the men grow by 10% and the women fall by 20%: the membership grows by %
Answer:
6.The distance grows 25% and the time taken falls 20%: the speed becomes times as much, % more.
Fill in each blank
Answer:
7.A club has 500 men and 300 women. This year the men grow by 15% and the women fall by 5%: the membership grows by %
Answer:

8.Over the same distance, a speed 150% higher cuts the time by 150%.
True or false?
Answer:
9.An item's price goes up 50% and its sales fall 25%. Its takings (price × number sold) become what percentage of before?
- A. 187.5%
- B. 125%
- C. 75%
- D. 112.5%
Choose the right answer
Answer:
10.Over the same distance, a speed 60% higher cuts the time by 37.5%.
True or false?
Answer:
11.An item's price goes up 20% and its sales fall 20%. Its takings (price × number sold) become what percentage of before?
- A. 96%
- B. 100%
- C. 80%
- D. 144%
Choose the right answer
Answer:
12.Takings = price × number sold. The price falls 20%. By what percentage must sales rise to keep the takings the same?
- A. 80%
- B. 20%
- C. 125%
- D. 25%
Choose the right answer
Answer:

13.Each side of a square rug is cut by 20%, so its area falls by 40%.
True or false?
Working:
Answer:
14.A shop's takings come from two kinds of goods, A and B, with A making 20% of the total. This year A's takings rise 25% and B's fall 5%. By what percentage do the total takings rise?
Working:
Answer:
15.A rectangular plot's length grows 50% and its width shrinks 25%. Find the percentage rise in its area: put the steps in order.
- A. Area factor = 1.5 × 0.75 = 1.125
- B. Percentage rise = 0.125 × 100% = 12.5%
- C. The rise = 1.125 − 1 = 0.125
Write the letters in the right order
Working:
Answer:
16.A rectangular garden is 22 m long and 8 m wide. With the length 20% longer and the width 10% narrower, what is the new area?
Working:
Answer:
17.A photo is enlarged so that its length and width are both 30% bigger. By what percentage does its area grow?
Working:
Answer:
18.A bakery puts its egg tarts up 25%, and daily sales fall from 200 to 160. Sales are down %, and the daily takings are % of before.
Fill in each blank
Working:
Answer:

Show the answers and working

Changes in the parts worksheet: Answers and working

1. 44
Takings = price × sales: (1 + 20%) × (1 + 20%) = 1 + 44%. The factors multiply, a little more than 20% + 20%.
2. 1.08, 8
Area = base × height ÷ 2, so the factors multiply: (1 + 20%) × (1 − 10%) = 1.08, 8% more.
3. 32
Takings = price × sales: (1 + 20%) × (1 + 10%) = 1 + 32%. The factors multiply, a little more than 20% + 10%.
4. 33.1
Volume = length × width × height, three factors multiplied: (1 + 10%)³ = 1 + 33.1%. Not 3 × 10% = 30%.
5. 2.5
900 × 10% = 90 more men and 300 × 20% = 60 fewer women: 30 more in all, and 30 ÷ 1200 × 100% = 2.5%. The two rates don't simply subtract.
6. 1.5625, 56.25
Speed = distance ÷ time, so the factors divide: (1 + 25%) ÷ (1 − 20%) = 1.5625, 56.25% more.
7. 7.5
500 × 15% = 75 more men and 300 × 5% = 15 fewer women: 60 more in all, and 60 ÷ 800 × 100% = 7.5%. The two rates don't simply subtract.

8. False
Time = distance ÷ speed, a factor of 1 ÷ (1 + 150%): the time becomes 40% of before, 60% less.
9. D. 112.5%
(1 + 50%) × (1 − 25%), that is 112.5% of before.
10. True
Time = distance ÷ speed, a factor of 1 ÷ (1 + 60%): the time becomes 62.5% of before, 37.5% less.
11. A. 96%
(1 + 20%) × (1 − 20%), that is 96% of before.
12. D. 25%
(1 − 20%) × the sales factor = 1, so sales must be 125% of before: up 25%.

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

13. False
The area's factor is 0.8 × 0.8, a fall of 36%, not 2 × 20% = 40%.
14. 1%
Say the total is 100: A brings 20 × 25% = 5 more, B 80 × 5% = 4 less, 1 more in all: 1%.
15. A → C → B
Multiply the length's and the width's factors, take 1 off, then turn it into a percentage.
16. 190.08 m²
New length 22 × (1 + 20%) = 26.4 m, new width 8 × (1 − 10%) = 7.2 m, area 26.4 × 7.2 = 190.08 m².
17. 69%
The area's factor is 1.3 × 1.3 = 1 + 69%, a 69% rise, not 2 × 30% = 60%.
18. 20, 100
Sales fell (200 − 160) ÷ 200 = 20%; the takings' factor is (1 + 25%) × (1 − 20%), 100% of before.

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