CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Which value of x makes the proportion 14:20 = 182:x true?
A. 262
B. 258
C. 34
D. 260
Correct Answer: D
14/20 = 182/x
Cross multiply: 14x = 20×182
x = (20×182) ÷ 14 = 260
Answer = 260
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 13:18 = 10.83:x, find x.
A. 15
B. 17
C. 31
D. 13
Correct Answer: A
13/18 = 10.83/x
Cross multiply: 13x = 18×10.83
x = (18×10.83) ÷ 13 = 15
Answer = 15
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 12:16 = 14:x, find x.
A. 16.67
B. 28
C. 20.67
D. 18.67
Correct Answer: D
12/16 = 14/x
Cross multiply: 12x = 16×14
x = (16×14) ÷ 12 = 18.67
Answer = 18.67
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If x:11 = 16:14, find x.
A. 25
B. 10.57
C. 14.57
D. 12.57
Correct Answer: D
x/11 = 16/14
Cross multiply: 14x = 11×16
x = (11×16) ÷ 14 = 12.57
Answer = 12.57
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Red and blue paints are mixed in the ratio 12:15. If 378 litres are prepared, how much blue paint is used?
A. 14 litres
B. 168 litres
C. 210 litres
D. 378 litres
Correct Answer: C
Total parts = 12+15 = 27
1 part = 378 ÷ 27 = 14 litres
Blue = 15 × 14 = 210 litres
Answer = 210 litres
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A model uses scale 1:13. If a model length is 24 cm, what is the actual length?
A. 13 cm
B. 312 cm
C. 325 cm
D. 24 cm
Correct Answer: B
Actual length = Model length × scale factor
= 24 × 13 = 312 cm
Answer = 312 cm
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A recipe uses flour and sugar in the ratio 11:14. If 165 cups of flour are used, how many cups of sugar are needed?
A. 14 cups
B. 212 cups
C. 165 cups
D. 210 cups
Correct Answer: D
11 parts = 165 cups
1 part = 165 ÷ 11 = 15.0 cups
Sugar = 14 parts = 210 cups
Answer = 210 cups
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A map scale is 1:110000. A distance is 12 cm on the map. What is the actual distance in kilometres?
A. 13.2 km
B. 14.2 km
C. 12 km
D. 12.2 km
Correct Answer: A
Actual distance = 12 × 110000 = 1320000 cm
1 km = 100,000 cm
Actual distance = 1320000 ÷ 100,000 = 13.2 km
Answer = 13.2 km
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 115% as a ratio in simplest form.
A. 23:20
B. 115:100
C. 1:1
D. 20:23
Correct Answer: A
115% = 115:100
HCF(115,100) = 5
Simplified ratio = 23:20
Answer = 23:20
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 110% as a ratio in simplest form.
A. 110:100
B. 10:11
C. 11:10
D. 1:1
Correct Answer: C
110% = 110:100
HCF(110,100) = 10
Simplified ratio = 11:10
Answer = 11:10
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 12:26, A is what percentage of B?
A. 31.58%
B. 12:26
C. 46.15%
D. 216.67%
Correct Answer: C
A as a percentage of B = (A ÷ B) × 100
= (12 ÷ 26) × 100 = 46.15%
Answer = 46.15%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 11:25, A is what percentage of B?
A. 30.56%
B. 227.27%
C. 44%
D. 11:25
Correct Answer: C
A as a percentage of B = (A ÷ B) × 100
= (11 ÷ 25) × 100 = 44%
Answer = 44%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Two rectangles measure 12×14 and 16×18. What is the ratio of their areas?
A. 7:12
B. 26:14
C. 40:26
D. 1:1
Correct Answer: A
Area₁ = 12×14 = 168
Area₂ = 16×18 = 288
Area ratio = 168:288 = 7:12
Answer = 7:12
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The edges of two cubes are in the ratio 13:25. What is the ratio of their volumes?
A. 1:1
B. 38:25
C. 2197:15625
D. 25:13
Correct Answer: C
Volume ∝ edge³
Volume ratio = 2197:15625 = 2197:15625
Answer = 2197:15625
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 12:24. What is the ratio of their areas?
A. 24:12
B. 1:4
C. 36:24
D. 1:1
Correct Answer: B
Area ∝ side²
Area ratio = 144:576 = 1:4
Answer = 1:4
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 11:23. What is the ratio of their perimeters?
A. 11:23
B. 1:1
C. 23:11
D. 34:23
Correct Answer: A
Perimeter of a square is directly proportional to its side.
Perimeter ratio = 11:23 = 11:23
Answer = 11:23
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 74,000 for 12 months and B invests Rs. 78,500 for 9 months. If total profit is Rs. 165,000, what is A's share?
A. Rs. 91890.87
B. Rs. 165,000
C. Rs. 82,500
D. Rs. 73109.13
Correct Answer: A
Profit ratio = 888000:706500 = 592:471
A's share = 888000/(888000+706500) × Rs. 165,000
= Rs. 91890.87
Answer = Rs. 91890.87
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 71,000 for 12 months and B invests Rs. 76,000 for 8 months. If total profit is Rs. 160,000, what is A's share?
A. Rs. 80,000
B. Rs. 66630.14
C. Rs. 160,000
D. Rs. 93369.86
Correct Answer: D
Profit ratio = 852000:608000 = 213:152
A's share = 852000/(852000+608000) × Rs. 160,000
= Rs. 93369.86
Answer = Rs. 93369.86
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 68,000 for 12 months and B invests Rs. 73,500 for 7 months. In what ratio should their profit be divided?
A. 544:343
B. 136:147
C. 12:7
D. 1:1
Correct Answer: A
A's capital-time = 68,000 × 12 = 816,000
B's capital-time = 73,500 × 7 = 514,500
Profit ratio = 816000:514500 = 544:343
Answer = 544:343
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 65,000 for 12 months and B invests Rs. 71,000 for 6 months. In what ratio should their profit be divided?
A. 2:1
B. 1:1
C. 65:71
D. 130:71
Correct Answer: D
A's capital-time = 65,000 × 12 = 780,000
B's capital-time = 71,000 × 6 = 426,000
Profit ratio = 780000:426000 = 130:71
Answer = 130:71