CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Which value of x makes the proportion 9:15 = 72:x true?
A. 118
B. 122
C. 24
D. 120
Correct Answer: D
9/15 = 72/x
Cross multiply: 9x = 15×72
x = (15×72) ÷ 9 = 120
Answer = 120
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 8:13 = 6.15:x, find x.
A. 8
B. 10
C. 12
D. 21
Correct Answer: B
8/13 = 6.15/x
Cross multiply: 8x = 13×6.15
x = (13×6.15) ÷ 8 = 10
Answer = 10
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 7:11 = 9:x, find x.
A. 18
B. 14.14
C. 16.14
D. 12.14
Correct Answer: B
7/11 = 9/x
Cross multiply: 7x = 11×9
x = (11×9) ÷ 7 = 14.14
Answer = 14.14
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If x:6 = 11:9, find x.
A. 9.33
B. 7.33
C. 15
D. 5.33
Correct Answer: B
x/6 = 11/9
Cross multiply: 9x = 6×11
x = (6×11) ÷ 9 = 7.33
Answer = 7.33
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Red and blue paints are mixed in the ratio 7:10. If 153 litres are prepared, how much blue paint is used?
A. 153 litres
B. 90 litres
C. 9 litres
D. 63 litres
Correct Answer: B
Total parts = 7+10 = 17
1 part = 153 ÷ 17 = 9 litres
Blue = 10 × 9 = 90 litres
Answer = 90 litres
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A model uses scale 1:8. If a model length is 19 cm, what is the actual length?
A. 8 cm
B. 160 cm
C. 152 cm
D. 19 cm
Correct Answer: C
Actual length = Model length × scale factor
= 19 × 8 = 152 cm
Answer = 152 cm
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A recipe uses flour and sugar in the ratio 6:9. If 60 cups of flour are used, how many cups of sugar are needed?
A. 60 cups
B. 92 cups
C. 90 cups
D. 9 cups
Correct Answer: C
6 parts = 60 cups
1 part = 60 ÷ 6 = 10.0 cups
Sugar = 9 parts = 90 cups
Answer = 90 cups
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A map scale is 1:60000. A distance is 7 cm on the map. What is the actual distance in kilometres?
A. 5.2 km
B. 4.2 km
C. 3.2 km
D. 7 km
Correct Answer: B
Actual distance = 7 × 60000 = 420000 cm
1 km = 100,000 cm
Actual distance = 420000 ÷ 100,000 = 4.2 km
Answer = 4.2 km
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 65% as a ratio in simplest form.
A. 20:13
B. 1:1
C. 13:20
D. 65:100
Correct Answer: C
65% = 65:100
HCF(65,100) = 5
Simplified ratio = 13:20
Answer = 13:20
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 60% as a ratio in simplest form.
A. 1:1
B. 3:5
C. 5:3
D. 60:100
Correct Answer: B
60% = 60:100
HCF(60,100) = 20
Simplified ratio = 3:5
Answer = 3:5
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 7:16, A is what percentage of B?
A. 228.57%
B. 7:16
C. 30.43%
D. 43.75%
Correct Answer: D
A as a percentage of B = (A ÷ B) × 100
= (7 ÷ 16) × 100 = 43.75%
Answer = 43.75%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 6:15, A is what percentage of B?
A. 40%
B. 250%
C. 6:15
D. 28.57%
Correct Answer: A
A as a percentage of B = (A ÷ B) × 100
= (6 ÷ 15) × 100 = 40%
Answer = 40%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Two rectangles measure 7×9 and 11×13. What is the ratio of their areas?
A. 16:9
B. 1:1
C. 63:143
D. 25:16
Correct Answer: C
Area₁ = 7×9 = 63
Area₂ = 11×13 = 143
Area ratio = 63:143 = 63:143
Answer = 63:143
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The edges of two cubes are in the ratio 8:15. What is the ratio of their volumes?
A. 15:8
B. 1:1
C. 512:3375
D. 23:15
Correct Answer: C
Volume ∝ edge³
Volume ratio = 512:3375 = 512:3375
Answer = 512:3375
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 7:14. What is the ratio of their areas?
A. 21:14
B. 1:4
C. 14:7
D. 1:1
Correct Answer: B
Area ∝ side²
Area ratio = 49:196 = 1:4
Answer = 1:4
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 6:13. What is the ratio of their perimeters?
A. 6:13
B. 19:13
C. 1:1
D. 13:6
Correct Answer: A
Perimeter of a square is directly proportional to its side.
Perimeter ratio = 6:13 = 6:13
Answer = 6:13
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 49,000 for 12 months and B invests Rs. 58,500 for 9 months. If total profit is Rs. 115,000, what is A's share?
A. Rs. 57,500
B. Rs. 115,000
C. Rs. 54327.05
D. Rs. 60672.95
Correct Answer: D
Profit ratio = 588000:526500 = 392:351
A's share = 588000/(588000+526500) × Rs. 115,000
= Rs. 60672.95
Answer = Rs. 60672.95
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 46,000 for 12 months and B invests Rs. 56,000 for 8 months. If total profit is Rs. 110,000, what is A's share?
A. Rs. 110,000
B. Rs. 60,720
C. Rs. 49,280
D. Rs. 55,000
Correct Answer: B
Profit ratio = 552000:448000 = 69:56
A's share = 552000/(552000+448000) × Rs. 110,000
= Rs. 60,720
Answer = Rs. 60,720
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 43,000 for 12 months and B invests Rs. 53,500 for 7 months. In what ratio should their profit be divided?
A. 1032:749
B. 1:1
C. 12:7
D. 86:107
Correct Answer: A
A's capital-time = 43,000 × 12 = 516,000
B's capital-time = 53,500 × 7 = 374,500
Profit ratio = 516000:374500 = 1032:749
Answer = 1032:749
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 40,000 for 12 months and B invests Rs. 51,000 for 6 months. In what ratio should their profit be divided?
A. 40:51
B. 1:1
C. 2:1
D. 80:51
Correct Answer: D
A's capital-time = 40,000 × 12 = 480,000
B's capital-time = 51,000 × 6 = 306,000
Profit ratio = 480000:306000 = 80:51
Answer = 80:51