Q.1 What is the ratio of 12 to 18 in simplest form?
2:3
3:2
4:6
6:9
Explanation - The GCD of 12 and 18 is 6. Dividing both by 6 gives 2:3.
Correct answer is: 2:3
Q.2 Express 45:60 in its lowest terms.
3:4
4:3
9:12
15:20
Explanation - The GCD of 45 and 60 is 15. Dividing both by 15 gives 3:4.
Correct answer is: 3:4
Q.3 If the ratio of boys to girls in a class is 5:3 and there are 40 students, how many boys are there?
25
30
20
35
Explanation - Total ratio = 5+3 = 8 parts. Each part = 40/8 = 5. Boys = 5×5 = 25.
Correct answer is: 25
Q.4 Simplify the ratio 150:200.
3:4
2:3
4:5
5:6
Explanation - The GCD of 150 and 200 is 50. Dividing gives 3:4.
Correct answer is: 3:4
Q.5 If 3 pens cost $18, what is the cost of 7 pens at the same rate?
$42
$36
$54
$48
Explanation - Cost per pen = $18 ÷ 3 = $6. Cost of 7 pens = 7 × $6 = $42.
Correct answer is: $42
Q.6 Divide 400 in the ratio 3:5.
150 and 250
120 and 280
100 and 300
200 and 200
Explanation - Sum of ratio = 3+5=8. Each part = 400÷8=50. 3 parts = 150, 5 parts = 250.
Correct answer is: 150 and 250
Q.7 A recipe needs ingredients in the ratio 2:3. If 200 g of the first ingredient is used, how much of the second ingredient is needed?
300 g
250 g
350 g
400 g
Explanation - Ratio factor = 200 ÷ 2 = 100. Second ingredient = 3 × 100 = 300 g.
Correct answer is: 300 g
Q.8 The sides of a rectangle are in the ratio 3:2. If the longer side is 24 cm, what is the shorter side?
12 cm
16 cm
18 cm
20 cm
Explanation - Ratio factor = 24 ÷ 3 = 8. Shorter side = 2 × 8 = 16 cm.
Correct answer is: 16 cm
Q.9 Simplify the ratio 81:108.
3:4
4:3
9:12
27:36
Explanation - The GCD of 81 and 108 is 27. Dividing gives 3:4.
Correct answer is: 3:4
Q.10 If the ratio of apples to oranges is 7:5 and there are 84 apples, how many oranges are there?
60
50
70
65
Explanation - Ratio factor = 84 ÷ 7 = 12. Oranges = 5 × 12 = 60.
Correct answer is: 60
Q.11 Simplify 72:96.
3:4
4:3
6:8
9:12
Explanation - The GCD of 72 and 96 is 24. Dividing gives 3:4.
Correct answer is: 3:4
Q.12 A sum of $720 is divided between A and B in the ratio 5:7. How much does B get?
$300
$420
$400
$500
Explanation - Total parts = 5+7=12. Each part = 720 ÷ 12 = 60. B = 7 × 60 = $420.
Correct answer is: $420
Q.13 Simplify 121:99.
11:9
9:11
22:18
33:27
Explanation - The GCD of 121 and 99 is 11. Dividing gives 11:9.
Correct answer is: 11:9
Q.14 The ratio of two numbers is 4:7. If the smaller number is 36, what is the larger?
63
72
54
84
Explanation - Ratio factor = 36 ÷ 4 = 9. Larger = 7 × 9 = 63.
Correct answer is: 63
Q.15 What is the ratio of 0.25 to 0.75?
1:3
3:1
2:3
1:2
Explanation - 0.25 ÷ 0.25 : 0.75 ÷ 0.25 = 1:3.
Correct answer is: 1:3
Q.16 Simplify 2.4:6.
2:5
1:2.5
4:10
12:30
Explanation - Dividing both terms by 1.2 gives 2:5.
Correct answer is: 2:5
Q.17 If a train covers 120 km in 2 hours, what distance will it cover in 5 hours at the same speed?
250 km
300 km
280 km
320 km
Explanation - Speed = 120 ÷ 2 = 60 km/h. Distance in 5 h = 60 × 5 = 300 km.
Correct answer is: 300 km
Q.18 Simplify 144:180.
4:5
5:4
6:8
12:15
Explanation - The GCD of 144 and 180 is 36. Dividing gives 4:5.
Correct answer is: 4:5
Q.19 Two numbers are in the ratio 7:9. Their sum is 128. Find the numbers.
56 and 72
54 and 74
60 and 68
64 and 72
Explanation - Sum of ratio parts = 7+9=16. Each part = 128 ÷ 16 = 8. Numbers = 56 and 72.
Correct answer is: 56 and 72
Q.20 Simplify 99:132.
3:4
4:3
11:14
33:44
Explanation - The GCD of 99 and 132 is 33. Dividing gives 3:4.
Correct answer is: 3:4
Q.21 If 15 workers can finish a task in 20 days, how many days will 30 workers take at the same rate?
10
20
15
25
Explanation - Work ∝ 1/No. of workers. Doubling workers halves time: 20 ÷ 2 = 10 days.
Correct answer is: 10
Q.22 If 5 kg of rice costs $200, what is the cost of 8 kg?
$320
$300
$250
$280
Explanation - Cost per kg = 200 ÷ 5 = 40. Cost of 8 kg = 8 × 40 = 320.
Correct answer is: $320
Q.23 Simplify 64:96.
2:3
3:2
4:6
8:12
Explanation - The GCD of 64 and 96 is 32. Dividing gives 2:3.
Correct answer is: 2:3
Q.24 If the ratio of ages of A and B is 3:5 and A is 24, what is B’s age?
36
30
40
45
Explanation - Ratio factor = 24 ÷ 3 = 8. B = 5 × 8 = 40.
Correct answer is: 40
Q.25 Simplify 225:300.
3:4
4:3
6:8
9:12
Explanation - The GCD of 225 and 300 is 75. Dividing gives 3:4.
Correct answer is: 3:4