Percentages and ratio · Ages 12–13

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Part of: Percentages (I)

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Percentages and ratio · Ages 12–13

Numsprite
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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 original x becomes 150% of itself, 270: x × 1.5 = 270, x =
Answer:
2.A number decreased by 50% is 40: 40 is % of the original, so the original = 40 ÷ = .
Fill in each blank
Answer:
3.A number decreased by 5% is 152: 152 is % of the original, so the original = 152 ÷ = .
Fill in each blank
Answer:
4.May is 15% taller than last year, 174.8 cm now. How tall was May last year?
Answer:
5.A number decreased by 15% is 493. The number was
Answer:
6.A number decreased by 20% is 416. The number was
Answer:
7.A number decreased by 75% is now 315 less than before. The number now =
Answer:

8.A number increased by 10% is 176, so the number was 160.
True or false?
Answer:
9.A number increased by 40% is 112. What was the number?
- A. 80
- B. 67.2
- C. 72
- D. 156.8
Choose the right answer
Answer:
10.A number increased by 40% is 168, so the number was 100.8.
True or false?
Answer:
11.A number increased by 50% is 360. What was the number?
- A. 240
- B. 540
- C. 180
- D. 310
Choose the right answer
Answer:
12.A number increased by 50% is now 120 more than before. What is the number now?
- A. 180
- B. 240
- C. 360
- D. 120
Choose the right answer
Answer:

13.A phone costs $7,440 after a 20% rise. With the old price $x: x × = 7440, x = .
Fill in each blank
Working:
Answer:
14.A coat sells for $773.5 after 15% off. What was its full price?
Working:
Answer:
15.After a 6% rise, Chi-keung's sister earns $22,790 a month. What did she earn before?
Working:
Answer:
16.A box of mooncakes went up 20%, which made it $16 dearer. What does a box cost now?
Working:
Answer:
17.An item sells for $240 after a 20% rise. Tsz-hin says: "The old price was 240 − 240 × 20% = 192." Which is right?
- A. Right; it was $192
- B. Wrong; it was $220
- C. Wrong; it was $200
- D. Wrong; it was $240
Choose the right answer
Working:
Answer:
18.Ka-yan has saved 20% more than Tsz-ching, and Ka-yan has $240. Tsz-ching has $, and Ka-yan has $ more.
Fill in each blank
Working:
Answer:

Show the answers and working

Back to the original value worksheet: Answers and working

1. 180
Divide both sides by 1.5: x = 270 ÷ 1.5 = 180.
2. 50, 0.5, 80
Down 50% leaves 100% − 50% = 50%, that is 0.5. 40 ÷ 0.5 = 80.
3. 95, 0.95, 160
Down 5% leaves 100% − 5% = 95%, that is 0.95. 152 ÷ 0.95 = 160.
4. 152 cm
Last year's height is the base: x × 1.15 = 174.8, so x = 174.8 ÷ 1.15 = 152.
5. 580
x × (1 − 15%) = 493, so x = 493 ÷ 0.85 = 580. Not 493 plus 15% of 493.
6. 520
x × (1 − 20%) = 416, so x = 416 ÷ 0.8 = 520. Not 416 plus 20% of 416.
7. 105
315 is 75% of the original: the original = 315 ÷ 75% = 420, and now it is 420 − 315 = 105.

8. True
The original = 176 ÷ 1.1 = 160. Taking 10% of 176 off 176 uses the wrong base.
9. A. 80
Let the original be x: x × 1.4 = 112, so x = 112 ÷ 1.4 = 80. Check: 80 × 1.4 = 112.
10. False
The original = 168 ÷ 1.4 = 120. Taking 40% of 168 off 168 uses the wrong base.
11. A. 240
Let the original be x: x × 1.5 = 360, so x = 360 ÷ 1.5 = 240. Check: 240 × 1.5 = 360.
12. C. 360
120 is 50% of the original, so the original = 120 ÷ 50% = 240, and now it is 240 + 120 = 360.

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

13. 1.2, 6,200
Up 20% is times 1.2: x = 7440 ÷ 1.2 = 6200.
14. 910 dollars
Full price × 0.85 = 773.5, so it was 773.5 ÷ 0.85 = 910. Not 773.5 × (1 + 15%).
15. 21,500 dollars
The rise is on the old pay: x × 1.06 = 22790, so x = 21500.
16. 96 dollars
$16 is 20% of the old price: it was 16 ÷ 20% = 80, and now 80 + 16 = 96.
17. C. Wrong; it was $200
Old price × (1 + 20%) = 240, so it was 200. Check: 20% of 200, added to 200, makes 240.
18. 200, 40
"More than Tsz-ching" takes Tsz-ching as the base: Tsz-ching's × (1 + 20%) = 240, so Tsz-ching has 200, 40 less.

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