1
The ratio of boys to girls in a class is 14:15. If there are 406 boys, how many girls are there?
Medium
ExplanationSince boys:girls = 14:15 and there are 406 boys, each 'part' = 406/14 = 29, so girls = 15 × 29 = 435.
Explanation1/5 of 205 = (1 × 205) / 5 = 41.
3
If 3:13 = 24:x, what is the value of x?
Medium
ExplanationSince 24/3 = 8, x = 13 × 8 = 104.
Explanation137.61 + 13.31 = 150.92.
5
Which is greater: 30.399 or 6.9?
Medium
ExplanationComparing digit by digit, 30.399 is greater than 6.9.
6
Which is greater: 34.88 or 38.855?
Medium
ExplanationComparing digit by digit, 38.855 is greater than 34.88.
7
Which is greater: 2 or 5?
Medium
Explanation2 = 2.0000 and 5 = 5.0000, so 5 is greater.
8
Which is greater: 5 or 2/3?
Medium
Explanation5 = 5.0000 and 2/3 = 0.6667, so 5 is greater.
ExplanationMultiply numerators and denominators: (11×5)/(12×8) = 55/96.
Explanation13.85 + 99.75 = 113.6.
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11
If 20 workers can complete a task in 34 days, how many days would 17 workers take to complete the same task (assuming the same work rate per worker)?
Medium
ExplanationTotal work = 20 × 34 = 680 worker-days. With 17 workers, days = 680/17 = 40.
12
A sum of Rs. 32 is divided between two people in the ratio 15:1. What is the larger share?
Medium
ExplanationTotal parts = 15 + 1 = 16. Each part = Rs. 32 / 16 = Rs. 2. So the shares are Rs. 30 and Rs. 2; the larger share is Rs. 30.
13
Convert the mixed number 8 11/12 to an improper fraction.
Medium
Explanation8 11/12 = ((8 × 12) + 11) / 12 = 107/12.
14
A car travels 160 km in 8 hours at a constant speed. How far will it travel in 10 hours?
Medium
ExplanationSpeed = 160 km / 8 hr = 20 km/hr. In 10 hours, distance = 20 × 10 = 200 km.
Explanation1/2 of 58 = (1 × 58) / 2 = 29.
16
A car travels 100 km in 10 hours at a constant speed. How far will it travel in 10 hours?
Medium
ExplanationSpeed = 100 km / 10 hr = 10 km/hr. In 10 hours, distance = 10 × 10 = 100 km.
ExplanationUsing a common denominator, 2/3 − 1/14 = 25/42.
Explanation67.38 + 43.11 = 110.49.
19
Convert the mixed number 1 6/7 to an improper fraction.
Medium
Explanation1 6/7 = ((1 × 7) + 6) / 7 = 13/7.
ExplanationMultiply numerators and denominators: (3×4)/(8×1) = 3/2.
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ExplanationMultiply numerators and denominators: (11×3)/(12×4) = 11/16.
22
A car travels 96 km in 6 hours at a constant speed. How far will it travel in 7 hours?
Medium
ExplanationSpeed = 96 km / 6 hr = 16 km/hr. In 7 hours, distance = 16 × 7 = 112 km.
Explanation1/9 of 450 = (1 × 450) / 9 = 50.
24
Convert the mixed number 8 2/5 to an improper fraction.
Medium
Explanation8 2/5 = ((8 × 5) + 2) / 5 = 42/5.
25
A sum of Rs. 672 is divided between two people in the ratio 5:9. What is the larger share?
Medium
ExplanationTotal parts = 5 + 9 = 14. Each part = Rs. 672 / 14 = Rs. 48. So the shares are Rs. 240 and Rs. 432; the larger share is Rs. 432.
ExplanationUsing a common denominator, 2 − 1/4 = 7/4.
27
A car travels 88 km in 8 hours at a constant speed. How far will it travel in 9 hours?
Medium
ExplanationSpeed = 88 km / 8 hr = 11 km/hr. In 9 hours, distance = 11 × 9 = 99 km.
28
The ratio of boys to girls in a class is 1:8. If there are 38 boys, how many girls are there?
Medium
ExplanationSince boys:girls = 1:8 and there are 38 boys, each 'part' = 38/1 = 38, so girls = 8 × 38 = 304.
ExplanationCross-multiplying: 7 × x = 3 × 105, so x = 315/7 = 45.
ExplanationDividing by a fraction means multiplying by its reciprocal: 3/2 × 5 = 15/2.
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31
If 10 pens cost Rs. 160, how much would 24 pens cost?
Medium
ExplanationCost per pen = Rs. 160/10 = Rs. 16. So 24 pens cost 24 × Rs. 16 = Rs. 384.
Explanation19.6 × 8.6 = 168.56.
Explanation277.97 − 1.11 = 276.86.
Explanation270.43 − 146.06 = 124.37.
Explanation8.6 × 15.2 = 130.72.
36
If A:B = 11:2 and B:C = 8:2, what is A:B:C?
Medium
ExplanationScale both ratios so B matches: A:B = 44:8 and B:C = 8:2, giving A:B:C = 44:8:2.
37
What is the reciprocal of 7/6?
Medium
ExplanationThe reciprocal of 7/6 is 6/7, since (7/6) × (6/7) = 1.
38
If A:B = 7:2 and B:C = 11:8, what is A:B:C?
Medium
ExplanationScale both ratios so B matches: A:B = 77:22 and B:C = 22:16, giving A:B:C = 77:22:16.
ExplanationDividing by a fraction means multiplying by its reciprocal: 11/5 × 5/3 = 11/3.
Explanation5/6 of 108 = (5 × 108) / 6 = 90.
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Explanation41.41 + 179.17 = 220.58.
42
What is the ratio of 175 to 200, expressed in lowest terms?
Medium
Explanation175:200 reduces by dividing both terms by their GCD (25), giving 7:8.
Explanation106.11 ÷ 13.1 = 8.1.
44
Simplify 4/2 to its lowest terms.
Medium
Explanation4 and 2 share a common factor of 2; dividing both by it gives 2.
45
What is the ratio of 78 to 26, expressed in lowest terms?
Medium
Explanation78:26 reduces by dividing both terms by their GCD (26), giving 3:1.
46
What is the reciprocal of 1/11?
Medium
ExplanationThe reciprocal of 1/11 is 11/1, since (1/11) × (11/1) = 1.
47
If 6 pens cost Rs. 84, how much would 25 pens cost?
Medium
ExplanationCost per pen = Rs. 84/6 = Rs. 14. So 25 pens cost 25 × Rs. 14 = Rs. 350.
48
Convert 113/12 to a mixed number.
Medium
Explanation113 ÷ 12 = 9 remainder 5, so 113/12 = 9 5/12.
ExplanationUsing a common denominator, 7/5 + 3/2 = 29/10.
ExplanationMultiply numerators and denominators: (1×5)/(6×2) = 5/12.
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51
If A:B = 7:6 and B:C = 2:6, what is A:B:C?
Medium
ExplanationScale both ratios so B matches: A:B = 7:6 and B:C = 6:18, giving A:B:C = 7:6:18.
ExplanationMultiply numerators and denominators: (7×3)/(12×8) = 7/32.
Explanation131.88 − 81.88 = 50.0.
54
If 20 workers can complete a task in 2 days, how many days would 40 workers take to complete the same task (assuming the same work rate per worker)?
Medium
ExplanationTotal work = 20 × 2 = 40 worker-days. With 40 workers, days = 40/40 = 1.
55
What is the ratio of 52 to 60, expressed in lowest terms?
Medium
Explanation52:60 reduces by dividing both terms by their GCD (4), giving 13:15.
56
Convert the mixed number 13 3/7 to an improper fraction.
Medium
Explanation13 3/7 = ((13 × 7) + 3) / 7 = 94/7.
ExplanationUsing a common denominator, 7/3 − 2/13 = 85/39.
58
The ratio of boys to girls in a class is 3:7. If there are 93 boys, how many girls are there?
Medium
ExplanationSince boys:girls = 3:7 and there are 93 boys, each 'part' = 93/3 = 31, so girls = 7 × 31 = 217.
Explanation192.26 + 53.21 = 245.47.
60
A car travels 6 km in 3 hours at a constant speed. How far will it travel in 2 hours?
Medium
ExplanationSpeed = 6 km / 3 hr = 2 km/hr. In 2 hours, distance = 2 × 2 = 4 km.
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61
Simplify 24/88 to its lowest terms.
Medium
Explanation24 and 88 share a common factor of 8; dividing both by it gives 3/11.
62
Round 281.4353 to the nearest tenth.
Medium
ExplanationRounding 281.4353 to the nearest tenth gives 281.4.
63
Solve for x: 8/15 = 200/x
Medium
ExplanationCross-multiplying: 8 × x = 15 × 200, so x = 3000/8 = 375.
64
What is 0.175 expressed as a fraction in lowest terms?
Medium
Explanation0.175 = 7/40, which reduces to 7/40 in lowest terms.
65
If 30 workers can complete a task in 35 days, how many days would 50 workers take to complete the same task (assuming the same work rate per worker)?
Medium
ExplanationTotal work = 30 × 35 = 1050 worker-days. With 50 workers, days = 1050/50 = 21.
Explanation3/8 of 472 = (3 × 472) / 8 = 177.
67
If A:B = 5:3 and B:C = 2:5, what is A:B:C?
Medium
ExplanationScale both ratios so B matches: A:B = 10:6 and B:C = 6:15, giving A:B:C = 10:6:15.
ExplanationDividing by a fraction means multiplying by its reciprocal: 3/2 × 11/3 = 11/2.
ExplanationMultiply numerators and denominators: (7×3)/(3×11) = 7/11.
70
What is the ratio of 33 to 15, expressed in lowest terms?
Medium
Explanation33:15 reduces by dividing both terms by their GCD (3), giving 11:5.
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71
Solve for x: 12/17 = 24/x
Medium
ExplanationCross-multiplying: 12 × x = 17 × 24, so x = 408/12 = 34.
72
Convert 59/8 to a mixed number.
Medium
Explanation59 ÷ 8 = 7 remainder 3, so 59/8 = 7 3/8.
73
A car travels 26 km in 2 hours at a constant speed. How far will it travel in 4 hours?
Medium
ExplanationSpeed = 26 km / 2 hr = 13 km/hr. In 4 hours, distance = 13 × 4 = 52 km.
74
A car travels 38 km in 2 hours at a constant speed. How far will it travel in 12 hours?
Medium
ExplanationSpeed = 38 km / 2 hr = 19 km/hr. In 12 hours, distance = 19 × 12 = 228 km.
Explanation193.94 − 143.94 = 50.0.
76
If 26 workers can complete a task in 18 days, how many days would 6 workers take to complete the same task (assuming the same work rate per worker)?
Medium
ExplanationTotal work = 26 × 18 = 468 worker-days. With 6 workers, days = 468/6 = 78.
77
Which is greater: 5/2 or 1/2?
Medium
Explanation5/2 = 2.5000 and 1/2 = 0.5000, so 5/2 is greater.
ExplanationMultiply numerators and denominators: (1×4)/(1×3) = 4/3.
79
Simplify 20/30 to its lowest terms.
Medium
Explanation20 and 30 share a common factor of 10; dividing both by it gives 2/3.
80
What is the reciprocal of 18/19?
Medium
ExplanationThe reciprocal of 18/19 is 19/18, since (18/19) × (19/18) = 1.
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81
What is 3/25 expressed as a decimal?
Medium
Explanation3 ÷ 25 = 0.12.
ExplanationUsing a common denominator, 11/14 + 1/8 = 51/56.
83
If 13 pens cost Rs. 312, how much would 9 pens cost?
Medium
ExplanationCost per pen = Rs. 312/13 = Rs. 24. So 9 pens cost 9 × Rs. 24 = Rs. 216.
Explanation2/3 of 27 = (2 × 27) / 3 = 18.
85
What is 14/25 expressed as a decimal?
Medium
Explanation14 ÷ 25 = 0.56.
Explanation240.39 − 190.39 = 50.0.
87
If A:B = 4:8 and B:C = 2:9, what is A:B:C?
Medium
ExplanationScale both ratios so B matches: A:B = 4:8 and B:C = 8:36, giving A:B:C = 4:8:36.
88
What is 0.24 expressed as a fraction in lowest terms?
Medium
Explanation0.24 = 24/100, which reduces to 6/25 in lowest terms.
89
What is the ratio of 171 to 72, expressed in lowest terms?
Medium
Explanation171:72 reduces by dividing both terms by their GCD (9), giving 19:8.
ExplanationCross-multiplying: 2 × x = 9 × 42, so x = 378/2 = 189.
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91
Which is greater: 12/5 or 1/14?
Medium
Explanation12/5 = 2.4000 and 1/14 = 0.0714, so 12/5 is greater.
92
If 5:8 = 35:x, what is the value of x?
Medium
ExplanationSince 35/5 = 7, x = 8 × 7 = 56.
93
What is the ratio of 48 to 320, expressed in lowest terms?
Medium
Explanation48:320 reduces by dividing both terms by their GCD (16), giving 3:20.
94
What is 11/25 expressed as a decimal?
Medium
Explanation11 ÷ 25 = 0.44.
ExplanationUsing a common denominator, 7/6 + 1/5 = 41/30.
96
Which is greater: 2.36 or 31.9?
Medium
ExplanationComparing digit by digit, 31.9 is greater than 2.36.
97
Round 154.6132 to the nearest hundredth.
Medium
ExplanationRounding 154.6132 to the nearest hundredth gives 154.61.
98
What is 0.925 expressed as a fraction in lowest terms?
Medium
Explanation0.925 = 37/40, which reduces to 37/40 in lowest terms.
99
Simplify 6/36 to its lowest terms.
Medium
Explanation6 and 36 share a common factor of 6; dividing both by it gives 1/6.
100
If 5:9 = 45:x, what is the value of x?
Medium
ExplanationSince 45/5 = 9, x = 9 × 9 = 81.