CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Which value of x makes the proportion 13:19 = 156:x true?
A. 32
B. 230
C. 228
D. 226
Correct Answer: C
13/19 = 156/x
Cross multiply: 13x = 19×156
x = (19×156) ÷ 13 = 228
Answer = 228
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 12:17 = 9.88:x, find x.
A. 29
B. 16
C. 14
D. 12
Correct Answer: C
12/17 = 9.88/x
Cross multiply: 12x = 17×9.88
x = (17×9.88) ÷ 12 = 14
Answer = 14
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 11:15 = 13:x, find x.
A. 26
B. 15.73
C. 19.73
D. 17.73
Correct Answer: D
11/15 = 13/x
Cross multiply: 11x = 15×13
x = (15×13) ÷ 11 = 17.73
Answer = 17.73
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If x:10 = 15:13, find x.
A. 11.54
B. 13.54
C. 23
D. 9.54
Correct Answer: A
x/10 = 15/13
Cross multiply: 13x = 10×15
x = (10×15) ÷ 13 = 11.54
Answer = 11.54
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Red and blue paints are mixed in the ratio 11:14. If 325 litres are prepared, how much blue paint is used?
A. 143 litres
B. 325 litres
C. 182 litres
D. 13 litres
Correct Answer: C
Total parts = 11+14 = 25
1 part = 325 ÷ 25 = 13 litres
Blue = 14 × 13 = 182 litres
Answer = 182 litres
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A model uses scale 1:12. If a model length is 23 cm, what is the actual length?
A. 276 cm
B. 12 cm
C. 288 cm
D. 23 cm
Correct Answer: A
Actual length = Model length × scale factor
= 23 × 12 = 276 cm
Answer = 276 cm
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A recipe uses flour and sugar in the ratio 10:13. If 140 cups of flour are used, how many cups of sugar are needed?
A. 184 cups
B. 140 cups
C. 182 cups
D. 13 cups
Correct Answer: C
10 parts = 140 cups
1 part = 140 ÷ 10 = 14.0 cups
Sugar = 13 parts = 182 cups
Answer = 182 cups
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A map scale is 1:100000. A distance is 11 cm on the map. What is the actual distance in kilometres?
A. None of these 1
B. 11 km
C. 10 km
D. 12 km
Correct Answer: B
Actual distance = 11 × 100000 = 1100000 cm
1 km = 100,000 cm
Actual distance = 1100000 ÷ 100,000 = 11 km
Answer = 11 km
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 105% as a ratio in simplest form.
A. 1:1
B. 105:100
C. 21:20
D. 20:21
Correct Answer: C
105% = 105:100
HCF(105,100) = 5
Simplified ratio = 21:20
Answer = 21:20
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 100% as a ratio in simplest form.
A. 100:100
B. None of these 2
C. None of these 1
D. 1:1
Correct Answer: D
100% = 100:100
HCF(100,100) = 100
Simplified ratio = 1:1
Answer = 1:1
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 11:24, A is what percentage of B?
A. 218.18%
B. 45.83%
C. 31.43%
D. 11:24
Correct Answer: B
A as a percentage of B = (A ÷ B) × 100
= (11 ÷ 24) × 100 = 45.83%
Answer = 45.83%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 10:23, A is what percentage of B?
A. 43.48%
B. 30.3%
C. 230%
D. 10:23
Correct Answer: A
A as a percentage of B = (A ÷ B) × 100
= (10 ÷ 23) × 100 = 43.48%
Answer = 43.48%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Two rectangles measure 11×13 and 15×17. What is the ratio of their areas?
A. 37:24
B. 1:1
C. 143:255
D. 24:13
Correct Answer: C
Area₁ = 11×13 = 143
Area₂ = 15×17 = 255
Area ratio = 143:255 = 143:255
Answer = 143:255
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The edges of two cubes are in the ratio 12:23. What is the ratio of their volumes?
A. 23:12
B. 35:23
C. 1728:12167
D. 1:1
Correct Answer: C
Volume ∝ edge³
Volume ratio = 1728:12167 = 1728:12167
Answer = 1728:12167
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 11:22. What is the ratio of their areas?
A. 1:4
B. 33:22
C. 1:1
D. 22:11
Correct Answer: A
Area ∝ side²
Area ratio = 121:484 = 1:4
Answer = 1:4
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 10:21. What is the ratio of their perimeters?
A. 1:1
B. 31:21
C. 10:21
D. 21:10
Correct Answer: C
Perimeter of a square is directly proportional to its side.
Perimeter ratio = 10:21 = 10:21
Answer = 10:21
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 69,000 for 12 months and B invests Rs. 74,500 for 9 months. If total profit is Rs. 155,000, what is A's share?
A. Rs. 69354.35
B. Rs. 77,500
C. Rs. 85645.65
D. Rs. 155,000
Correct Answer: C
Profit ratio = 828000:670500 = 184:149
A's share = 828000/(828000+670500) × Rs. 155,000
= Rs. 85645.65
Answer = Rs. 85645.65
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 66,000 for 12 months and B invests Rs. 72,000 for 8 months. If total profit is Rs. 150,000, what is A's share?
A. Rs. 86842.11
B. Rs. 63157.89
C. Rs. 75,000
D. Rs. 150,000
Correct Answer: A
Profit ratio = 792000:576000 = 11:8
A's share = 792000/(792000+576000) × Rs. 150,000
= Rs. 86842.11
Answer = Rs. 86842.11
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 63,000 for 12 months and B invests Rs. 69,500 for 7 months. In what ratio should their profit be divided?
A. 1:1
B. 126:139
C. 216:139
D. 12:7
Correct Answer: C
A's capital-time = 63,000 × 12 = 756,000
B's capital-time = 69,500 × 7 = 486,500
Profit ratio = 756000:486500 = 216:139
Answer = 216:139
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 60,000 for 12 months and B invests Rs. 67,000 for 6 months. In what ratio should their profit be divided?
A. 120:67
B. 1:1
C. 60:67
D. 2:1
Correct Answer: A
A's capital-time = 60,000 × 12 = 720,000
B's capital-time = 67,000 × 6 = 402,000
Profit ratio = 720000:402000 = 120:67
Answer = 120:67