CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Which value of x makes the proportion 7:13 = 42:x true?
A. 20
B. 80
C. 78
D. 76
Correct Answer: C
7/13 = 42/x
Cross multiply: 7x = 13×42
x = (13×42) ÷ 7 = 78
Answer = 78
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 6:11 = 4.36:x, find x.
A. 8
B. 6
C. 17
D. 10
Correct Answer: A
6/11 = 4.36/x
Cross multiply: 6x = 11×4.36
x = (11×4.36) ÷ 6 = 8
Answer = 8
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If 5:9 = 7:x, find x.
A. 14.6
B. 10.6
C. 12.6
D. 14
Correct Answer: C
5/9 = 7/x
Cross multiply: 5x = 9×7
x = (9×7) ÷ 5 = 12.6
Answer = 12.6
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If x:4 = 9:7, find x.
A. 11
B. 5.14
C. 7.14
D. 3.14
Correct Answer: B
x/4 = 9/7
Cross multiply: 7x = 4×9
x = (4×9) ÷ 7 = 5.14
Answer = 5.14
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Red and blue paints are mixed in the ratio 5:8. If 91 litres are prepared, how much blue paint is used?
A. 91 litres
B. 7 litres
C. 56 litres
D. 35 litres
Correct Answer: C
Total parts = 5+8 = 13
1 part = 91 ÷ 13 = 7 litres
Blue = 8 × 7 = 56 litres
Answer = 56 litres
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A model uses scale 1:6. If a model length is 17 cm, what is the actual length?
A. 17 cm
B. 102 cm
C. 108 cm
D. 6 cm
Correct Answer: B
Actual length = Model length × scale factor
= 17 × 6 = 102 cm
Answer = 102 cm
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A recipe uses flour and sugar in the ratio 4:7. If 32 cups of flour are used, how many cups of sugar are needed?
A. 56 cups
B. 58 cups
C. 32 cups
D. 7 cups
Correct Answer: A
4 parts = 32 cups
1 part = 32 ÷ 4 = 8.0 cups
Sugar = 7 parts = 56 cups
Answer = 56 cups
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A map scale is 1:40000. A distance is 5 cm on the map. What is the actual distance in kilometres?
A. 3 km
B. 1 km
C. 2 km
D. 5 km
Correct Answer: C
Actual distance = 5 × 40000 = 200000 cm
1 km = 100,000 cm
Actual distance = 200000 ÷ 100,000 = 2 km
Answer = 2 km
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 45% as a ratio in simplest form.
A. 9:20
B. 1:1
C. 20:9
D. 45:100
Correct Answer: A
45% = 45:100
HCF(45,100) = 5
Simplified ratio = 9:20
Answer = 9:20
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Express 40% as a ratio in simplest form.
A. 5:2
B. 40:100
C. 1:1
D. 2:5
Correct Answer: D
40% = 40:100
HCF(40,100) = 20
Simplified ratio = 2:5
Answer = 2:5
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 5:12, A is what percentage of B?
A. 240%
B. 41.67%
C. 5:12
D. 29.41%
Correct Answer: B
A as a percentage of B = (A ÷ B) × 100
= (5 ÷ 12) × 100 = 41.67%
Answer = 41.67%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
If A:B = 4:11, A is what percentage of B?
A. 275%
B. 26.67%
C. 4:11
D. 36.36%
Correct Answer: D
A as a percentage of B = (A ÷ B) × 100
= (4 ÷ 11) × 100 = 36.36%
Answer = 36.36%
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
Two rectangles measure 5×7 and 9×11. What is the ratio of their areas?
A. 1:1
B. 12:7
C. 19:12
D. 35:99
Correct Answer: D
Area₁ = 5×7 = 35
Area₂ = 9×11 = 99
Area ratio = 35:99 = 35:99
Answer = 35:99
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The edges of two cubes are in the ratio 6:11. What is the ratio of their volumes?
A. 11:6
B. 17:11
C. 1:1
D. 216:1331
Correct Answer: D
Volume ∝ edge³
Volume ratio = 216:1331 = 216:1331
Answer = 216:1331
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 5:10. What is the ratio of their areas?
A. 10:5
B. 1:1
C. 15:10
D. 1:4
Correct Answer: D
Area ∝ side²
Area ratio = 25:100 = 1:4
Answer = 1:4
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
The sides of two squares are in the ratio 4:9. What is the ratio of their perimeters?
A. 1:1
B. 9:4
C. 13:9
D. 4:9
Correct Answer: D
Perimeter of a square is directly proportional to its side.
Perimeter ratio = 4:9 = 4:9
Answer = 4:9
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 39,000 for 12 months and B invests Rs. 50,500 for 9 months. If total profit is Rs. 95,000, what is A's share?
A. Rs. 48195.12
B. Rs. 47,500
C. Rs. 46804.88
D. Rs. 95,000
Correct Answer: A
Profit ratio = 468000:454500 = 104:101
A's share = 468000/(468000+454500) × Rs. 95,000
= Rs. 48195.12
Answer = Rs. 48195.12
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 36,000 for 12 months and B invests Rs. 48,000 for 8 months. If total profit is Rs. 90,000, what is A's share?
A. Rs. 45,000
B. Rs. 47647.06
C. Rs. 90,000
D. Rs. 42352.94
Correct Answer: B
Profit ratio = 432000:384000 = 9:8
A's share = 432000/(432000+384000) × Rs. 90,000
= Rs. 47647.06
Answer = Rs. 47647.06
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 33,000 for 12 months and B invests Rs. 45,500 for 7 months. In what ratio should their profit be divided?
A. 12:7
B. 66:91
C. 792:637
D. 1:1
Correct Answer: C
A's capital-time = 33,000 × 12 = 396,000
B's capital-time = 45,500 × 7 = 318,500
Profit ratio = 396000:318500 = 792:637
Answer = 792:637
CSS - PMS - CCE - PCS - Mathematics
Ratio & Proportion
A invests Rs. 30,000 for 12 months and B invests Rs. 43,000 for 6 months. In what ratio should their profit be divided?
A. 30:43
B. 1:1
C. 2:1
D. 60:43
Correct Answer: D
A's capital-time = 30,000 × 12 = 360,000
B's capital-time = 43,000 × 6 = 258,000
Profit ratio = 360000:258000 = 60:43
Answer = 60:43