Mock Test Ultimate Proportional Reasoning Practice Test for Class 8 Chapter-7

Ganita Prakash | Class 8 | Chapter - 7

Section A: Multiple Choice (Choose one)

1. Simplify the ratio 84:126.

• A) 2:3
• B) 4:6
• C) 3:2
• D) 1:2

2. Are the ratios 6:10 and 24:40 proportional?

• A) Yes
• B) No

3. In 7:21::x:63, the value of x is:

• A) 14
• B) 21
• C) 18
• D) 27

4. A builder uses 12 bags of cement for a 48 m wall. How many bags for a 60 m wall at the same strength?

• A) 12
• B) 14
• C) 15
• D) 20

5. If 24x​=6015​, then x=

• A) 6
• B) 8
• C) 12
• D) 10

6. A profit of $4,000 is shared in the ratio 3:1. The larger share is:

• A) $2,500
• B) $3,000
• C) $2,000
• D) $1,000

7. Convert 0.75 kg to grams.

• A) 7.5 g
• B) 75 g
• C) 750 g
• D) 7,500 g

8. Which is more expensive per 100 g?
   Tea A: $12 for 300 g; Tea B: $18 for 500 g.

• A) Tea A
• B) Tea B
• C) Equal
• D) Cannot say

9. Which change preserves similarity of a rectangle that is 16 cm by 12 cm?

• A) Width +4 cm, height +3 cm
• B) Width ×1.5, height ×1.25
• C) Width ×2, height ×2
• D) Width +2 cm, height ×2

10. A drink has sugar:water = 1:4. If you make 3 L total, how much sugar is needed?

• A) 0.6 L
• B) 0.75 L
• C) 0.8 L
• D) 0.5 L

Section B: Fill in the Blanks (Show working)

11. Complete the proportion: 14:21::x:42. Find x.

12. Divide 72 pens among A, B, C in the ratio 2:3:1. How many does each receive?

13. A mixture has sand:cement = 3:1 and total mass 40 kg. Find kg of sand and kg of cement.

14. If 15 kg rice is needed for 120 students, how many kg are needed for 200 students?

Section C: Short Answer

15. Check whether 18:24 and 27:36 are proportional. Explain briefly.

16. Find y so that 9:y::12:32.

17. A scooter covers 36 km in 45 minutes at constant speed. How far will it travel in 2 hours?

18. A 5 m ribbon costs $7.50. At the same rate, what is the cost of 18 m?

Section D: Word Problems (Show steps)

19. A school maintains a teacher:student ratio of 1:25. If there are 14 teachers, how many students are there? If 2 teachers leave but students remain the same, what is the new simplified ratio?

20. Paint mix ratio is blue:white = 2:5. You currently have 6 L of blue and 10 L of white. To reach exactly the 2:5 ratio without changing the blue amount, how much white should you have, and how much more white must be added?

21. A shop sells coffee packs:

• Pack A: 250 g for $7.25
• Pack B: 400 g for $10.80
  Which pack has the lower price per kilogram? Show calculation.

22. The width:height ratio of a signboard is 5:3. If the height is 54 cm, find the width. Then explain why adding 10 cm to both width and height would not preserve the ratio.

Answer Key (with brief workings)

1. A. 84:126=(84÷42):(126÷42)=2:3

2. A. 6:10→3:5; 24:40→3:5. Same simplest form.

3. B. Factor from 21 to 63 is ×3; so x=7×3=21.

4. C. 4812​=60x​⇒x=12×4860​=15.

5. A. x×60=15×24⇒x=60360​=6.

6. B. Total parts =3+1=4. Each part = $4,000 ÷ 4 = $1,000. Larger share = 3×$1,000=$3,000.

7. C. 0.75 kg =750 g.

8. A. A: 30012​×100=$4 per 100 g; B: 50018​×100=$3.6 per 100 g. Tea A is more expensive.

9. C. Multiplying both dimensions by the same factor preserves similarity.

10. A. Parts =1+4=5. Sugar =51​×3 L =0.6 L.

11. 14:21::x:42. Simplify 14:21 → 2:3. For 42 as second term: 3k=42⇒k=14. So x=2k=28.

12. Total parts =2+3+1=6. Each part =72÷6=12.

• A: 2×12=24
• B: 3×12=36
• C: 1×12=12

13. Parts =3+1=4. Each part =40÷4=10.

• Sand =3×10=30 kg
• Cement =1×10=10 kg

14. 12015​=200x​⇒x=15×120200​=25 kg.

15. Simplify: 18:24→3:4; 27:36→3:4. Yes, proportional (same simplest form).

16. 9:y=12:32⇒9×32=12y⇒y=12288​=24.

17. Convert 2 h → 120 min. 4536​=120x​⇒x=36×45120​=96 km.

18. Unit rate: $7.50÷5 m =$1.50 per m. Cost for 18 m =18×$1.50=$27.

19. Students =14×25=350. If 2 teachers leave: 12 teachers, 350 students. Ratio =12:350→6:175.

20. Blue 6 L corresponds to 2 parts → 1 part =3 L. White needs 5 parts =5×3=15 L. Currently white = 10 L. Need to add 15−10=5 L.

21. Price per kg:

• A: $7.25 ÷ 0.25 kg =$29.00 per kg
• B: $10.80 ÷ 0.40 kg =$27.00 per kg
  Pack B is cheaper.

22. Height 54 cm corresponds to 3 parts → 1 part =18 cm. Width =5×18=90 cm. Adding 10 cm to both gives 100:64, which is not equal to 5:3 (ratio changes), so similarity is not preserved.