CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Which value of x makes the proportion 10:16 = 90:x true?
A. 146
B. 144
C. 26
D. 142
Correct Answer: B
10/16 = 90/x
Cross multiply: 10x = 16×90
x = (16×90) ÷ 10 = 144
Answer = 144
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 9:14 = 7.07:x, find x.
A. 23
B. 11
C. 13
D. 9
Correct Answer: B
9/14 = 7.07/x
Cross multiply: 9x = 14×7.07
x = (14×7.07) ÷ 9 = 11
Answer = 11
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 8:12 = 10:x, find x.
A. 20
B. 15
C. 13
D. 17
Correct Answer: B
8/12 = 10/x
Cross multiply: 8x = 12×10
x = (12×10) ÷ 8 = 15
Answer = 15
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If x:7 = 12:10, find x.
A. 8.4
B. 6.4
C. 17
D. 10.4
Correct Answer: A
x/7 = 12/10
Cross multiply: 10x = 7×12
x = (7×12) ÷ 10 = 8.4
Answer = 8.4
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Red and blue paints are mixed in the ratio 8:11. If 190 litres are prepared, how much blue paint is used?
A. 110 litres
B. 190 litres
C. 10 litres
D. 80 litres
Correct Answer: A
Total parts = 8+11 = 19
1 part = 190 ÷ 19 = 10 litres
Blue = 11 × 10 = 110 litres
Answer = 110 litres
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A model uses scale 1:9. If a model length is 20 cm, what is the actual length?
A. 20 cm
B. 9 cm
C. 189 cm
D. 180 cm
Correct Answer: D
Actual length = Model length × scale factor
= 20 × 9 = 180 cm
Answer = 180 cm
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A recipe uses flour and sugar in the ratio 7:10. If 77 cups of flour are used, how many cups of sugar are needed?
A. 77 cups
B. 112 cups
C. 10 cups
D. 110 cups
Correct Answer: D
7 parts = 77 cups
1 part = 77 ÷ 7 = 11.0 cups
Sugar = 10 parts = 110 cups
Answer = 110 cups
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A map scale is 1:70000. A distance is 8 cm on the map. What is the actual distance in kilometres?
A. 6.6 km
B. 8 km
C. 4.6 km
D. 5.6 km
Correct Answer: D
Actual distance = 8 × 70000 = 560000 cm
1 km = 100,000 cm
Actual distance = 560000 ÷ 100,000 = 5.6 km
Answer = 5.6 km
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 75% as a ratio in simplest form.
A. 1:1
B. 75:100
C. 4:3
D. 3:4
Correct Answer: D
75% = 75:100
HCF(75,100) = 25
Simplified ratio = 3:4
Answer = 3:4
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 70% as a ratio in simplest form.
A. 10:7
B. 7:10
C. 1:1
D. 70:100
Correct Answer: B
70% = 70:100
HCF(70,100) = 10
Simplified ratio = 7:10
Answer = 7:10
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 8:18, A is what percentage of B?
A. 30.77%
B. 225%
C. 44.44%
D. 8:18
Correct Answer: C
A as a percentage of B = (A ÷ B) × 100
= (8 ÷ 18) × 100 = 44.44%
Answer = 44.44%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 7:17, A is what percentage of B?
A. 7:17
B. 41.18%
C. 242.86%
D. 29.17%
Correct Answer: B
A as a percentage of B = (A ÷ B) × 100
= (7 ÷ 17) × 100 = 41.18%
Answer = 41.18%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Two rectangles measure 8×10 and 12×14. What is the ratio of their areas?
A. 1:1
B. 28:18
C. 18:10
D. 10:21
Correct Answer: D
Area₁ = 8×10 = 80
Area₂ = 12×14 = 168
Area ratio = 80:168 = 10:21
Answer = 10:21
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The edges of two cubes are in the ratio 9:17. What is the ratio of their volumes?
A. 729:4913
B. 1:1
C. 17:9
D. 26:17
Correct Answer: A
Volume ∝ edge³
Volume ratio = 729:4913 = 729:4913
Answer = 729:4913
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 8:16. What is the ratio of their areas?
A. 1:1
B. 24:16
C. 16:8
D. 1:4
Correct Answer: D
Area ∝ side²
Area ratio = 64:256 = 1:4
Answer = 1:4
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 7:15. What is the ratio of their perimeters?
A. 7:15
B. 15:7
C. 1:1
D. 22:15
Correct Answer: A
Perimeter of a square is directly proportional to its side.
Perimeter ratio = 7:15 = 7:15
Answer = 7:15
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 54,000 for 12 months and B invests Rs. 62,500 for 9 months. If total profit is Rs. 125,000, what is A's share?
A. Rs. 58085.5
B. Rs. 66914.5
C. Rs. 62,500
D. Rs. 125,000
Correct Answer: B
Profit ratio = 648000:562500 = 144:125
A's share = 648000/(648000+562500) × Rs. 125,000
= Rs. 66914.5
Answer = Rs. 66914.5
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 51,000 for 12 months and B invests Rs. 60,000 for 8 months. If total profit is Rs. 120,000, what is A's share?
A. Rs. 120,000
B. Rs. 60,000
C. Rs. 52747.25
D. Rs. 67252.75
Correct Answer: D
Profit ratio = 612000:480000 = 51:40
A's share = 612000/(612000+480000) × Rs. 120,000
= Rs. 67252.75
Answer = Rs. 67252.75
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 48,000 for 12 months and B invests Rs. 57,500 for 7 months. In what ratio should their profit be divided?
A. 1152:805
B. 12:7
C. 1:1
D. 96:115
Correct Answer: A
A's capital-time = 48,000 × 12 = 576,000
B's capital-time = 57,500 × 7 = 402,500
Profit ratio = 576000:402500 = 1152:805
Answer = 1152:805
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 45,000 for 12 months and B invests Rs. 55,000 for 6 months. In what ratio should their profit be divided?
A. 9:11
B. 1:1
C. 18:11
D. 2:1
Correct Answer: C
A's capital-time = 45,000 × 12 = 540,000
B's capital-time = 55,000 × 6 = 330,000
Profit ratio = 540000:330000 = 18:11
Answer = 18:11