CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Which value of x makes the proportion 8:14 = 56:x true?
A. 100
B. 96
C. 22
D. 98
Correct Answer: D
8/14 = 56/x
Cross multiply: 8x = 14×56
x = (14×56) ÷ 8 = 98
Answer = 98
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 7:12 = 5.25:x, find x.
A. 11
B. 9
C. 7
D. 19
Correct Answer: B
7/12 = 5.25/x
Cross multiply: 7x = 12×5.25
x = (12×5.25) ÷ 7 = 9
Answer = 9
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 6:10 = 8:x, find x.
A. 11.33
B. 15.33
C. 13.33
D. 16
Correct Answer: C
6/10 = 8/x
Cross multiply: 6x = 10×8
x = (10×8) ÷ 6 = 13.33
Answer = 13.33
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If x:5 = 10:8, find x.
A. 4.25
B. 6.25
C. 13
D. 8.25
Correct Answer: B
x/5 = 10/8
Cross multiply: 8x = 5×10
x = (5×10) ÷ 8 = 6.25
Answer = 6.25
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Red and blue paints are mixed in the ratio 6:9. If 120 litres are prepared, how much blue paint is used?
A. 72 litres
B. 120 litres
C. 48 litres
D. 8 litres
Correct Answer: A
Total parts = 6+9 = 15
1 part = 120 ÷ 15 = 8 litres
Blue = 9 × 8 = 72 litres
Answer = 72 litres
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A model uses scale 1:7. If a model length is 18 cm, what is the actual length?
A. 126 cm
B. 133 cm
C. 7 cm
D. 18 cm
Correct Answer: A
Actual length = Model length × scale factor
= 18 × 7 = 126 cm
Answer = 126 cm
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A recipe uses flour and sugar in the ratio 5:8. If 45 cups of flour are used, how many cups of sugar are needed?
A. 74 cups
B. 72 cups
C. 45 cups
D. 8 cups
Correct Answer: B
5 parts = 45 cups
1 part = 45 ÷ 5 = 9.0 cups
Sugar = 8 parts = 72 cups
Answer = 72 cups
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A map scale is 1:50000. A distance is 6 cm on the map. What is the actual distance in kilometres?
A. 4 km
B. 3 km
C. 2 km
D. 6 km
Correct Answer: B
Actual distance = 6 × 50000 = 300000 cm
1 km = 100,000 cm
Actual distance = 300000 ÷ 100,000 = 3 km
Answer = 3 km
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 55% as a ratio in simplest form.
A. 55:100
B. 1:1
C. 11:20
D. 20:11
Correct Answer: C
55% = 55:100
HCF(55,100) = 5
Simplified ratio = 11:20
Answer = 11:20
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 50% as a ratio in simplest form.
A. 2:1
B. 1:1
C. 1:2
D. 50:100
Correct Answer: C
50% = 50:100
HCF(50,100) = 50
Simplified ratio = 1:2
Answer = 1:2
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 6:14, A is what percentage of B?
A. 42.86%
B. 233.33%
C. 30%
D. 6:14
Correct Answer: A
A as a percentage of B = (A ÷ B) × 100
= (6 ÷ 14) × 100 = 42.86%
Answer = 42.86%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 5:13, A is what percentage of B?
A. 27.78%
B. 5:13
C. 260%
D. 38.46%
Correct Answer: D
A as a percentage of B = (A ÷ B) × 100
= (5 ÷ 13) × 100 = 38.46%
Answer = 38.46%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Two rectangles measure 6×8 and 10×12. What is the ratio of their areas?
A. 22:14
B. 14:8
C. 2:5
D. 1:1
Correct Answer: C
Area₁ = 6×8 = 48
Area₂ = 10×12 = 120
Area ratio = 48:120 = 2:5
Answer = 2:5
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The edges of two cubes are in the ratio 7:13. What is the ratio of their volumes?
A. 20:13
B. 343:2197
C. 13:7
D. 1:1
Correct Answer: B
Volume ∝ edge³
Volume ratio = 343:2197 = 343:2197
Answer = 343:2197
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 6:12. What is the ratio of their areas?
A. 12:6
B. 18:12
C. 1:1
D. 1:4
Correct Answer: D
Area ∝ side²
Area ratio = 36:144 = 1:4
Answer = 1:4
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 5:11. What is the ratio of their perimeters?
A. 1:1
B. 11:5
C. 16:11
D. 5:11
Correct Answer: D
Perimeter of a square is directly proportional to its side.
Perimeter ratio = 5:11 = 5:11
Answer = 5:11
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 44,000 for 12 months and B invests Rs. 54,500 for 9 months. If total profit is Rs. 105,000, what is A's share?
A. Rs. 50567.01
B. Rs. 54432.99
C. Rs. 52,500
D. Rs. 105,000
Correct Answer: B
Profit ratio = 528000:490500 = 352:327
A's share = 528000/(528000+490500) × Rs. 105,000
= Rs. 54432.99
Answer = Rs. 54432.99
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 41,000 for 12 months and B invests Rs. 52,000 for 8 months. If total profit is Rs. 100,000, what is A's share?
A. Rs. 100,000
B. Rs. 45814.98
C. Rs. 50,000
D. Rs. 54185.02
Correct Answer: D
Profit ratio = 492000:416000 = 123:104
A's share = 492000/(492000+416000) × Rs. 100,000
= Rs. 54185.02
Answer = Rs. 54185.02
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 38,000 for 12 months and B invests Rs. 49,500 for 7 months. In what ratio should their profit be divided?
A. 12:7
B. 304:231
C. 76:99
D. 1:1
Correct Answer: B
A's capital-time = 38,000 × 12 = 456,000
B's capital-time = 49,500 × 7 = 346,500
Profit ratio = 456000:346500 = 304:231
Answer = 304:231
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 35,000 for 12 months and B invests Rs. 47,000 for 6 months. In what ratio should their profit be divided?
A. 1:1
B. 35:47
C. 2:1
D. 70:47
Correct Answer: D
A's capital-time = 35,000 × 12 = 420,000
B's capital-time = 47,000 × 6 = 282,000
Profit ratio = 420000:282000 = 70:47
Answer = 70:47