CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Which value of x makes the proportion 6:12 = 30:x true?
A. 58
B. 60
C. 62
D. 18
Correct Answer: B
6/12 = 30/x
Cross multiply: 6x = 12×30
x = (12×30) ÷ 6 = 60
Answer = 60
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 5:10 = 3.5:x, find x.
A. 7
B. 5
C. 9
D. 15
Correct Answer: A
5/10 = 3.5/x
Cross multiply: 5x = 10×3.5
x = (10×3.5) ÷ 5 = 7
Answer = 7
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 4:8 = 6:x, find x.
A. 12
B. 10
C. 14
D. None of these 1
Correct Answer: A
4/8 = 6/x
Cross multiply: 4x = 8×6
x = (8×6) ÷ 4 = 12
Answer = 12
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If x:3 = 8:6, find x.
A. 6
B. 2
C. 9
D. 4
Correct Answer: D
x/3 = 8/6
Cross multiply: 6x = 3×8
x = (3×8) ÷ 6 = 4
Answer = 4
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Red and blue paints are mixed in the ratio 4:7. If 66 litres are prepared, how much blue paint is used?
A. 66 litres
B. 24 litres
C. 42 litres
D. 6 litres
Correct Answer: C
Total parts = 4+7 = 11
1 part = 66 ÷ 11 = 6 litres
Blue = 7 × 6 = 42 litres
Answer = 42 litres
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A model uses scale 1:5. If a model length is 16 cm, what is the actual length?
A. 5 cm
B. 85 cm
C. 16 cm
D. 80 cm
Correct Answer: D
Actual length = Model length × scale factor
= 16 × 5 = 80 cm
Answer = 80 cm
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A recipe uses flour and sugar in the ratio 3:6. If 21 cups of flour are used, how many cups of sugar are needed?
A. 6 cups
B. 21 cups
C. 44 cups
D. 42 cups
Correct Answer: D
3 parts = 21 cups
1 part = 21 ÷ 3 = 7.0 cups
Sugar = 6 parts = 42 cups
Answer = 42 cups
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A map scale is 1:30000. A distance is 4 cm on the map. What is the actual distance in kilometres?
A. 4 km
B. 0.2 km
C. 2.2 km
D. 1.2 km
Correct Answer: D
Actual distance = 4 × 30000 = 120000 cm
1 km = 100,000 cm
Actual distance = 120000 ÷ 100,000 = 1.2 km
Answer = 1.2 km
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 35% as a ratio in simplest form.
A. 7:20
B. 35:100
C. 20:7
D. 1:1
Correct Answer: A
35% = 35:100
HCF(35,100) = 5
Simplified ratio = 7:20
Answer = 7:20
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 30% as a ratio in simplest form.
A. 10:3
B. 1:1
C. 30:100
D. 3:10
Correct Answer: D
30% = 30:100
HCF(30,100) = 10
Simplified ratio = 3:10
Answer = 3:10
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 4:10, A is what percentage of B?
A. 250%
B. 28.57%
C. 4:10
D. 40%
Correct Answer: D
A as a percentage of B = (A ÷ B) × 100
= (4 ÷ 10) × 100 = 40%
Answer = 40%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 3:9, A is what percentage of B?
A. 25%
B. 3:9
C. 33.33%
D. 300%
Correct Answer: C
A as a percentage of B = (A ÷ B) × 100
= (3 ÷ 9) × 100 = 33.33%
Answer = 33.33%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Two rectangles measure 4×6 and 8×10. What is the ratio of their areas?
A. 1:1
B. 16:10
C. 3:10
D. 10:6
Correct Answer: C
Area₁ = 4×6 = 24
Area₂ = 8×10 = 80
Area ratio = 24:80 = 3:10
Answer = 3:10
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The edges of two cubes are in the ratio 5:9. What is the ratio of their volumes?
A. 14:9
B. 9:5
C. 1:1
D. 125:729
Correct Answer: D
Volume ∝ edge³
Volume ratio = 125:729 = 125:729
Answer = 125:729
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 4:8. What is the ratio of their areas?
A. 8:4
B. 1:1
C. 12:8
D. 1:4
Correct Answer: D
Area ∝ side²
Area ratio = 16:64 = 1:4
Answer = 1:4
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 3:7. What is the ratio of their perimeters?
A. 3:7
B. 1:1
C. 10:7
D. 7:3
Correct Answer: A
Perimeter of a square is directly proportional to its side.
Perimeter ratio = 3:7 = 3:7
Answer = 3:7
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 34,000 for 12 months and B invests Rs. 46,500 for 9 months. If total profit is Rs. 85,000, what is A's share?
A. Rs. 42,500
B. Rs. 41960.07
C. Rs. 85,000
D. Rs. 43039.93
Correct Answer: B
Profit ratio = 408000:418500 = 272:279
A's share = 408000/(408000+418500) × Rs. 85,000
= Rs. 41960.07
Answer = Rs. 41960.07
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 31,000 for 12 months and B invests Rs. 44,000 for 8 months. If total profit is Rs. 80,000, what is A's share?
A. Rs. 80,000
B. Rs. 38895.03
C. Rs. 40,000
D. Rs. 41104.97
Correct Answer: D
Profit ratio = 372000:352000 = 93:88
A's share = 372000/(372000+352000) × Rs. 80,000
= Rs. 41104.97
Answer = Rs. 41104.97
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 28,000 for 12 months and B invests Rs. 41,500 for 7 months. In what ratio should their profit be divided?
A. 12:7
B. 56:83
C. 96:83
D. 1:1
Correct Answer: C
A's capital-time = 28,000 × 12 = 336,000
B's capital-time = 41,500 × 7 = 290,500
Profit ratio = 336000:290500 = 96:83
Answer = 96:83
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 25,000 for 12 months and B invests Rs. 39,000 for 6 months. In what ratio should their profit be divided?
A. 50:39
B. 2:1
C. 1:1
D. 25:39
Correct Answer: A
A's capital-time = 25,000 × 12 = 300,000
B's capital-time = 39,000 × 6 = 234,000
Profit ratio = 300000:234000 = 50:39
Answer = 50:39