CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Which value of x makes the proportion 12:18 = 132:x true?
A. 200
B. 196
C. 198
D. 30
Correct Answer: C
12/18 = 132/x
Cross multiply: 12x = 18×132
x = (18×132) ÷ 12 = 198
Answer = 198
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 11:16 = 8.94:x, find x.
A. 27
B. 11
C. 13
D. 15
Correct Answer: C
11/16 = 8.94/x
Cross multiply: 11x = 16×8.94
x = (16×8.94) ÷ 11 = 13
Answer = 13
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 10:14 = 12:x, find x.
A. 18.8
B. 16.8
C. 14.8
D. 24
Correct Answer: B
10/14 = 12/x
Cross multiply: 10x = 14×12
x = (14×12) ÷ 10 = 16.8
Answer = 16.8
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If x:9 = 14:12, find x.
A. 21
B. 10.5
C. 8.5
D. 12.5
Correct Answer: B
x/9 = 14/12
Cross multiply: 12x = 9×14
x = (9×14) ÷ 12 = 10.5
Answer = 10.5
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Red and blue paints are mixed in the ratio 10:13. If 276 litres are prepared, how much blue paint is used?
A. 156 litres
B. 12 litres
C. 276 litres
D. 120 litres
Correct Answer: A
Total parts = 10+13 = 23
1 part = 276 ÷ 23 = 12 litres
Blue = 13 × 12 = 156 litres
Answer = 156 litres
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A model uses scale 1:11. If a model length is 22 cm, what is the actual length?
A. 22 cm
B. 242 cm
C. 253 cm
D. 11 cm
Correct Answer: B
Actual length = Model length × scale factor
= 22 × 11 = 242 cm
Answer = 242 cm
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A recipe uses flour and sugar in the ratio 9:12. If 117 cups of flour are used, how many cups of sugar are needed?
A. 156 cups
B. 12 cups
C. 158 cups
D. 117 cups
Correct Answer: A
9 parts = 117 cups
1 part = 117 ÷ 9 = 13.0 cups
Sugar = 12 parts = 156 cups
Answer = 156 cups
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A map scale is 1:90000. A distance is 10 cm on the map. What is the actual distance in kilometres?
A. 10 km
B. 9 km
C. 8 km
D. None of these 1
Correct Answer: B
Actual distance = 10 × 90000 = 900000 cm
1 km = 100,000 cm
Actual distance = 900000 ÷ 100,000 = 9 km
Answer = 9 km
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 95% as a ratio in simplest form.
A. 19:20
B. 95:100
C. 1:1
D. 20:19
Correct Answer: A
95% = 95:100
HCF(95,100) = 5
Simplified ratio = 19:20
Answer = 19:20
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 90% as a ratio in simplest form.
A. 90:100
B. 10:9
C. 9:10
D. 1:1
Correct Answer: C
90% = 90:100
HCF(90,100) = 10
Simplified ratio = 9:10
Answer = 9:10
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 10:22, A is what percentage of B?
A. 220%
B. 10:22
C. 45.45%
D. 31.25%
Correct Answer: C
A as a percentage of B = (A ÷ B) × 100
= (10 ÷ 22) × 100 = 45.45%
Answer = 45.45%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 9:21, A is what percentage of B?
A. 233.33%
B. 9:21
C. 30%
D. 42.86%
Correct Answer: D
A as a percentage of B = (A ÷ B) × 100
= (9 ÷ 21) × 100 = 42.86%
Answer = 42.86%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Two rectangles measure 10×12 and 14×16. What is the ratio of their areas?
A. 34:22
B. 15:28
C. 22:12
D. 1:1
Correct Answer: B
Area₁ = 10×12 = 120
Area₂ = 14×16 = 224
Area ratio = 120:224 = 15:28
Answer = 15:28
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The edges of two cubes are in the ratio 11:21. What is the ratio of their volumes?
A. 32:21
B. 1:1
C. 1331:9261
D. 21:11
Correct Answer: C
Volume ∝ edge³
Volume ratio = 1331:9261 = 1331:9261
Answer = 1331:9261
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 10:20. What is the ratio of their areas?
A. 20:10
B. 1:1
C. 30:20
D. 1:4
Correct Answer: D
Area ∝ side²
Area ratio = 100:400 = 1:4
Answer = 1:4
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 9:19. What is the ratio of their perimeters?
A. 1:1
B. 28:19
C. 19:9
D. 9:19
Correct Answer: D
Perimeter of a square is directly proportional to its side.
Perimeter ratio = 9:19 = 9:19
Answer = 9:19
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 64,000 for 12 months and B invests Rs. 70,500 for 9 months. If total profit is Rs. 145,000, what is A's share?
A. Rs. 145,000
B. Rs. 65598.93
C. Rs. 79401.07
D. Rs. 72,500
Correct Answer: C
Profit ratio = 768000:634500 = 512:423
A's share = 768000/(768000+634500) × Rs. 145,000
= Rs. 79401.07
Answer = Rs. 79401.07
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 61,000 for 12 months and B invests Rs. 68,000 for 8 months. If total profit is Rs. 140,000, what is A's share?
A. Rs. 59686.52
B. Rs. 80313.48
C. Rs. 70,000
D. Rs. 140,000
Correct Answer: B
Profit ratio = 732000:544000 = 183:136
A's share = 732000/(732000+544000) × Rs. 140,000
= Rs. 80313.48
Answer = Rs. 80313.48
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 58,000 for 12 months and B invests Rs. 65,500 for 7 months. In what ratio should their profit be divided?
A. 12:7
B. 1:1
C. 116:131
D. 1392:917
Correct Answer: D
A's capital-time = 58,000 × 12 = 696,000
B's capital-time = 65,500 × 7 = 458,500
Profit ratio = 696000:458500 = 1392:917
Answer = 1392:917
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 55,000 for 12 months and B invests Rs. 63,000 for 6 months. In what ratio should their profit be divided?
A. 1:1
B. 55:63
C. 110:63
D. 2:1
Correct Answer: C
A's capital-time = 55,000 × 12 = 660,000
B's capital-time = 63,000 × 6 = 378,000
Profit ratio = 660000:378000 = 110:63
Answer = 110:63