CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Which value of x makes the proportion 11:17 = 110:x true?
A. 28
B. 170
C. 168
D. 172
Correct Answer: B
11/17 = 110/x
Cross multiply: 11x = 17×110
x = (17×110) ÷ 11 = 170
Answer = 170
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 10:15 = 8:x, find x.
A. 10
B. 14
C. 12
D. 25
Correct Answer: C
10/15 = 8/x
Cross multiply: 10x = 15×8
x = (15×8) ÷ 10 = 12
Answer = 12
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 9:13 = 11:x, find x.
A. 22
B. 13.89
C. 15.89
D. 17.89
Correct Answer: C
9/13 = 11/x
Cross multiply: 9x = 13×11
x = (13×11) ÷ 9 = 15.89
Answer = 15.89
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If x:8 = 13:11, find x.
A. 11.45
B. 7.45
C. 9.45
D. 19
Correct Answer: C
x/8 = 13/11
Cross multiply: 11x = 8×13
x = (8×13) ÷ 11 = 9.45
Answer = 9.45
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Red and blue paints are mixed in the ratio 9:12. If 231 litres are prepared, how much blue paint is used?
A. 231 litres
B. 132 litres
C. 11 litres
D. 99 litres
Correct Answer: B
Total parts = 9+12 = 21
1 part = 231 ÷ 21 = 11 litres
Blue = 12 × 11 = 132 litres
Answer = 132 litres
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A model uses scale 1:10. If a model length is 21 cm, what is the actual length?
A. 220 cm
B. 21 cm
C. 10 cm
D. 210 cm
Correct Answer: D
Actual length = Model length × scale factor
= 21 × 10 = 210 cm
Answer = 210 cm
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A recipe uses flour and sugar in the ratio 8:11. If 96 cups of flour are used, how many cups of sugar are needed?
A. 96 cups
B. 11 cups
C. 132 cups
D. 134 cups
Correct Answer: C
8 parts = 96 cups
1 part = 96 ÷ 8 = 12.0 cups
Sugar = 11 parts = 132 cups
Answer = 132 cups
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A map scale is 1:80000. A distance is 9 cm on the map. What is the actual distance in kilometres?
A. 9 km
B. 6.2 km
C. 8.2 km
D. 7.2 km
Correct Answer: D
Actual distance = 9 × 80000 = 720000 cm
1 km = 100,000 cm
Actual distance = 720000 ÷ 100,000 = 7.2 km
Answer = 7.2 km
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 85% as a ratio in simplest form.
A. 17:20
B. 85:100
C. 1:1
D. 20:17
Correct Answer: A
85% = 85:100
HCF(85,100) = 5
Simplified ratio = 17:20
Answer = 17:20
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 80% as a ratio in simplest form.
A. 4:5
B. 80:100
C. 1:1
D. 5:4
Correct Answer: A
80% = 80:100
HCF(80,100) = 20
Simplified ratio = 4:5
Answer = 4:5
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 9:20, A is what percentage of B?
A. 45%
B. 9:20
C. 31.03%
D. 222.22%
Correct Answer: A
A as a percentage of B = (A ÷ B) × 100
= (9 ÷ 20) × 100 = 45%
Answer = 45%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 8:19, A is what percentage of B?
A. 29.63%
B. 237.5%
C. 8:19
D. 42.11%
Correct Answer: D
A as a percentage of B = (A ÷ B) × 100
= (8 ÷ 19) × 100 = 42.11%
Answer = 42.11%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Two rectangles measure 9×11 and 13×15. What is the ratio of their areas?
A. 33:65
B. 20:11
C. 31:20
D. 1:1
Correct Answer: A
Area₁ = 9×11 = 99
Area₂ = 13×15 = 195
Area ratio = 99:195 = 33:65
Answer = 33:65
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The edges of two cubes are in the ratio 10:19. What is the ratio of their volumes?
A. 19:10
B. 1:1
C. 29:19
D. 1000:6859
Correct Answer: D
Volume ∝ edge³
Volume ratio = 1000:6859 = 1000:6859
Answer = 1000:6859
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 9:18. What is the ratio of their areas?
A. 1:1
B. 1:4
C. 27:18
D. 18:9
Correct Answer: B
Area ∝ side²
Area ratio = 81:324 = 1:4
Answer = 1:4
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 8:17. What is the ratio of their perimeters?
A. 25:17
B. 17:8
C. 8:17
D. 1:1
Correct Answer: C
Perimeter of a square is directly proportional to its side.
Perimeter ratio = 8:17 = 8:17
Answer = 8:17
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 59,000 for 12 months and B invests Rs. 66,500 for 9 months. If total profit is Rs. 135,000, what is A's share?
A. Rs. 73157.29
B. Rs. 67,500
C. Rs. 61842.71
D. Rs. 135,000
Correct Answer: A
Profit ratio = 708000:598500 = 472:399
A's share = 708000/(708000+598500) × Rs. 135,000
= Rs. 73157.29
Answer = Rs. 73157.29
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 56,000 for 12 months and B invests Rs. 64,000 for 8 months. If total profit is Rs. 130,000, what is A's share?
A. Rs. 130,000
B. Rs. 65,000
C. Rs. 56216.22
D. Rs. 73783.78
Correct Answer: D
Profit ratio = 672000:512000 = 21:16
A's share = 672000/(672000+512000) × Rs. 130,000
= Rs. 73783.78
Answer = Rs. 73783.78
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 53,000 for 12 months and B invests Rs. 61,500 for 7 months. In what ratio should their profit be divided?
A. 106:123
B. 424:287
C. 1:1
D. 12:7
Correct Answer: B
A's capital-time = 53,000 × 12 = 636,000
B's capital-time = 61,500 × 7 = 430,500
Profit ratio = 636000:430500 = 424:287
Answer = 424:287
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 50,000 for 12 months and B invests Rs. 59,000 for 6 months. In what ratio should their profit be divided?
A. 50:59
B. 1:1
C. 100:59
D. 2:1
Correct Answer: C
A's capital-time = 50,000 × 12 = 600,000
B's capital-time = 59,000 × 6 = 354,000
Profit ratio = 600000:354000 = 100:59
Answer = 100:59