CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Which value of x makes the proportion 5:11 = 20:x true?
A. 44
B. 16
C. 46
D. 42
Correct Answer: A
5/11 = 20/x
Cross multiply: 5x = 11×20
x = (11×20) ÷ 5 = 44
Answer = 44
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 4:9 = 2.67:x, find x.
A. 6
B. 13
C. 4
D. 8
Correct Answer: A
4/9 = 2.67/x
Cross multiply: 4x = 9×2.67
x = (9×2.67) ÷ 4 = 6
Answer = 6
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 3:7 = 5:x, find x.
A. 11.67
B. 9.67
C. 13.67
D. 10
Correct Answer: A
3/7 = 5/x
Cross multiply: 3x = 7×5
x = (7×5) ÷ 3 = 11.67
Answer = 11.67
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If x:2 = 7:5, find x.
A. 2.8
B. 7
C. 4.8
D. 0.8
Correct Answer: A
x/2 = 7/5
Cross multiply: 5x = 2×7
x = (2×7) ÷ 5 = 2.8
Answer = 2.8
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Red and blue paints are mixed in the ratio 3:6. If 45 litres are prepared, how much blue paint is used?
A. 15 litres
B. 45 litres
C. 30 litres
D. 5 litres
Correct Answer: C
Total parts = 3+6 = 9
1 part = 45 ÷ 9 = 5 litres
Blue = 6 × 5 = 30 litres
Answer = 30 litres
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A model uses scale 1:4. If a model length is 15 cm, what is the actual length?
A. 15 cm
B. 64 cm
C. 60 cm
D. 4 cm
Correct Answer: C
Actual length = Model length × scale factor
= 15 × 4 = 60 cm
Answer = 60 cm
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A recipe uses flour and sugar in the ratio 2:5. If 12 cups of flour are used, how many cups of sugar are needed?
A. 12 cups
B. 5 cups
C. 30 cups
D. 32 cups
Correct Answer: C
2 parts = 12 cups
1 part = 12 ÷ 2 = 6.0 cups
Sugar = 5 parts = 30 cups
Answer = 30 cups
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A map scale is 1:20000. A distance is 3 cm on the map. What is the actual distance in kilometres?
A. 3 km
B. 0.6 km
C. 1.6 km
D. 0 km
Correct Answer: B
Actual distance = 3 × 20000 = 60000 cm
1 km = 100,000 cm
Actual distance = 60000 ÷ 100,000 = 0.6 km
Answer = 0.6 km
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 25% as a ratio in simplest form.
A. 1:1
B. 25:100
C. 4:1
D. 1:4
Correct Answer: D
25% = 25:100
HCF(25,100) = 25
Simplified ratio = 1:4
Answer = 1:4
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 20% as a ratio in simplest form.
A. 20:100
B. 1:5
C. 1:1
D. 5:1
Correct Answer: B
20% = 20:100
HCF(20,100) = 20
Simplified ratio = 1:5
Answer = 1:5
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 3:8, A is what percentage of B?
A. 27.27%
B. 3:8
C. 266.67%
D. 37.5%
Correct Answer: D
A as a percentage of B = (A ÷ B) × 100
= (3 ÷ 8) × 100 = 37.5%
Answer = 37.5%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 2:7, A is what percentage of B?
A. 350%
B. 2:7
C. 22.22%
D. 28.57%
Correct Answer: D
A as a percentage of B = (A ÷ B) × 100
= (2 ÷ 7) × 100 = 28.57%
Answer = 28.57%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Two rectangles measure 3×5 and 7×9. What is the ratio of their areas?
A. 13:8
B. 8:5
C. 5:21
D. 1:1
Correct Answer: C
Area₁ = 3×5 = 15
Area₂ = 7×9 = 63
Area ratio = 15:63 = 5:21
Answer = 5:21
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The edges of two cubes are in the ratio 4:7. What is the ratio of their volumes?
A. 64:343
B. 11:7
C. 7:4
D. 1:1
Correct Answer: A
Volume ∝ edge³
Volume ratio = 64:343 = 64:343
Answer = 64:343
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 3:6. What is the ratio of their areas?
A. 1:1
B. 1:4
C. 6:3
D. 9:6
Correct Answer: B
Area ∝ side²
Area ratio = 9:36 = 1:4
Answer = 1:4
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 2:5. What is the ratio of their perimeters?
A. 1:1
B. 2:5
C. 7:5
D. 5:2
Correct Answer: B
Perimeter of a square is directly proportional to its side.
Perimeter ratio = 2:5 = 2:5
Answer = 2:5
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 29,000 for 12 months and B invests Rs. 42,500 for 9 months. If total profit is Rs. 75,000, what is A's share?
A. Rs. 37,500
B. Rs. 39271.05
C. Rs. 35728.95
D. Rs. 75,000
Correct Answer: C
Profit ratio = 348000:382500 = 232:255
A's share = 348000/(348000+382500) × Rs. 75,000
= Rs. 35728.95
Answer = Rs. 35728.95
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 26,000 for 12 months and B invests Rs. 40,000 for 8 months. If total profit is Rs. 70,000, what is A's share?
A. Rs. 70,000
B. Rs. 34556.96
C. Rs. 35,000
D. Rs. 35443.04
Correct Answer: B
Profit ratio = 312000:320000 = 39:40
A's share = 312000/(312000+320000) × Rs. 70,000
= Rs. 34556.96
Answer = Rs. 34556.96
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 23,000 for 12 months and B invests Rs. 37,500 for 7 months. In what ratio should their profit be divided?
A. 1:1
B. 184:175
C. 46:75
D. 12:7
Correct Answer: B
A's capital-time = 23,000 × 12 = 276,000
B's capital-time = 37,500 × 7 = 262,500
Profit ratio = 276000:262500 = 184:175
Answer = 184:175
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 20,000 for 12 months and B invests Rs. 35,000 for 6 months. In what ratio should their profit be divided?
A. 8:7
B. 4:7
C. 2:1
D. 1:1
Correct Answer: A
A's capital-time = 20,000 × 12 = 240,000
B's capital-time = 35,000 × 6 = 210,000
Profit ratio = 240000:210000 = 8:7
Answer = 8:7