Ratios Competitive Exams
100 questions · Mathematics
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Question 1 of 100
If 4:2 :: 10:x, find the value of x.
ExplanationIn a proportion, product of extremes = product of means: 4 x x = 2 x 10 => x = 20/4 = 5.
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Question 2 of 100
If A:B = 7:6 and A = 42, find the value of B.
ExplanationSince A:B = 7:6, B = A x (6/7) = 42 x 6/7 = 36.
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Question 3 of 100
A sum of Rs. 156 is divided among P, Q and R in the ratio 3:6:4. What is Q's share?
ExplanationTotal parts = 3+6+4 = 13. Value of 1 part = 156/13 = 12. Q's share = 6 x 12 = Rs. 72.
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Question 4 of 100
Divide Rs. 169 between A and B in the ratio 9:4. What is A's share?
ExplanationTotal parts = 9+4 = 13. Value of 1 part = 169/13 = 13. A's share = 9 x 13 = Rs. 117.
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Question 5 of 100
A sum of Rs. 162 is divided among P, Q and R in the ratio 6:2:1. What is Q's share?
ExplanationTotal parts = 6+2+1 = 9. Value of 1 part = 162/9 = 18. Q's share = 2 x 18 = Rs. 36.
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Question 6 of 100
In a class, the ratio of boys to girls is 7:3. If the total number of students is 250, find the number of girls.
ExplanationTotal parts = 7+3 = 10. Value of 1 part = 250/10 = 25. Number of girls = 3 x 25 = 75.
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Question 7 of 100
In a factory, the ratio of male to female workers is 5:6. If there are 100 male workers, how many female workers are there?
ExplanationSince male:female = 5:6, and male = 100, one part = 100/5 = 20. Female workers = 6 x 20 = 120.
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Question 8 of 100
Find the mean proportional between 10 and 10.
ExplanationMean proportional = sqrt(10 x 10) = sqrt(100) = 10.
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Question 9 of 100
Which ratio is greater: 1:2 or 3:5?
Explanation1:2 = 0.500, 3:5 = 0.600. Since 0.600 > 0.500, the greater ratio is 3:5.
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Question 10 of 100
If A:B = 3:2 and B:C = 4:5, find A:B:C.
ExplanationLCM of B-values (2 and 4) = 4. Scale A:B = 6:4 and B:C = 4:5. So A:B:C = 6:4:5 (in lowest terms).
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Question 11 of 100
Which ratio is greater: 4:7 or 5:9?
Explanation4:7 = 0.571, 5:9 = 0.556. Since 0.571 > 0.556, the greater ratio is 4:7.
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Question 12 of 100
If A:B = 4:9 and A = 52, find the value of B.
ExplanationSince A:B = 4:9, B = A x (9/4) = 52 x 9/4 = 117.
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Question 13 of 100
Two cars cover the same distance in the ratio of times 3:10. What is the ratio of their speeds?
ExplanationFor the same distance, speed is inversely proportional to time. So speed ratio = 10:3 (inverse of time ratio 3:10), simplified = 10:3.
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Question 14 of 100
Simplify the ratio 66:55 to its lowest terms.
ExplanationHCF of 66 and 55 is 11. Dividing both terms: 66/11 : 55/11 = 6:5.
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Question 15 of 100
Two cars cover the same distance in the ratio of times 6:5. What is the ratio of their speeds?
ExplanationFor the same distance, speed is inversely proportional to time. So speed ratio = 5:6 (inverse of time ratio 6:5), simplified = 5:6.
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Question 16 of 100
In a factory, the ratio of male to female workers is 7:4. If there are 91 male workers, how many female workers are there?
ExplanationSince male:female = 7:4, and male = 91, one part = 91/7 = 13. Female workers = 4 x 13 = 52.
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Question 17 of 100
A sum of Rs. 32 is divided among P, Q and R in the ratio 1:5:2. What is Q's share?
ExplanationTotal parts = 1+5+2 = 8. Value of 1 part = 32/8 = 4. Q's share = 5 x 4 = Rs. 20.
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Question 18 of 100
Two numbers are in the ratio 5:2. If their difference is 12, find the larger number.
ExplanationLet numbers be 5x and 2x. Difference = (5-2)x = 12 => x = 4. Larger number = 5 x 4 = 20.
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Question 19 of 100
In a class, the ratio of boys to girls is 4:9. If the total number of students is 273, find the number of girls.
ExplanationTotal parts = 4+9 = 13. Value of 1 part = 273/13 = 21. Number of girls = 9 x 21 = 189.
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Question 20 of 100
The income and expenditure of a person are in the ratio 5:4. If his income is Rs. 3090, find his savings.
ExplanationLet income = 5x, expenditure = 4x. Given 5x = 3090 => x = 618. Expenditure = 4 x 618 = 2472. Savings = Income - Expenditure = 3090 - 2472 = Rs. 618.
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Question 21 of 100
Which ratio is greater: 2:5 or 3:7?
Explanation2:5 = 0.400, 3:7 = 0.429. Since 0.429 > 0.400, the greater ratio is 3:7.
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Question 22 of 100
If A:B = 3:2 and A = 15, find the value of B.
ExplanationSince A:B = 3:2, B = A x (2/3) = 15 x 2/3 = 10.
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Question 23 of 100
Divide Rs. 175 between A and B in the ratio 4:3. What is A's share?
ExplanationTotal parts = 4+3 = 7. Value of 1 part = 175/7 = 25. A's share = 4 x 25 = Rs. 100.
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Question 24 of 100
Two cars cover the same distance in the ratio of times 5:8. What is the ratio of their speeds?
ExplanationFor the same distance, speed is inversely proportional to time. So speed ratio = 8:5 (inverse of time ratio 5:8), simplified = 8:5.
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Question 25 of 100
If 3:5 :: 12:x, find the value of x.
ExplanationIn a proportion, product of extremes = product of means: 3 x x = 5 x 12 => x = 60/3 = 20.
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Question 26 of 100
Simplify the ratio 110:70 to its lowest terms.
ExplanationHCF of 110 and 70 is 10. Dividing both terms: 110/10 : 70/10 = 11:7.
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Question 27 of 100
In a factory, the ratio of male to female workers is 9:2. If there are 189 male workers, how many female workers are there?
ExplanationSince male:female = 9:2, and male = 189, one part = 189/9 = 21. Female workers = 2 x 21 = 42.
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Question 28 of 100
Which ratio is greater: 3:4 or 5:6?
Explanation3:4 = 0.750, 5:6 = 0.833. Since 0.833 > 0.750, the greater ratio is 5:6.
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Question 29 of 100
Simplify the ratio 130:117 to its lowest terms.
ExplanationHCF of 130 and 117 is 13. Dividing both terms: 130/13 : 117/13 = 10:9.
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Question 30 of 100
Two cars cover the same distance in the ratio of times 4:7. What is the ratio of their speeds?
ExplanationFor the same distance, speed is inversely proportional to time. So speed ratio = 7:4 (inverse of time ratio 4:7), simplified = 7:4.
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Question 31 of 100
If A:B = 8:5 and A = 104, find the value of B.
ExplanationSince A:B = 8:5, B = A x (5/8) = 104 x 5/8 = 65.
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Question 32 of 100
If 10:3 :: 10:x, find the value of x.
ExplanationIn a proportion, product of extremes = product of means: 10 x x = 3 x 10 => x = 30/10 = 3.
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Question 33 of 100
A sum of Rs. 77 is divided among P, Q and R in the ratio 3:2:2. What is Q's share?
ExplanationTotal parts = 3+2+2 = 7. Value of 1 part = 77/7 = 11. Q's share = 2 x 11 = Rs. 22.
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Question 34 of 100
The ages of two persons are in the ratio 3:7. If the sum of their ages is 30 years, find the age of the elder person.
ExplanationLet ages be 3x and 7x. Sum = 10x = 30 => x = 3. Elder's age = 7 x 3 = 21 years.
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Question 35 of 100
Divide Rs. 156 between A and B in the ratio 5:7. What is A's share?
ExplanationTotal parts = 5+7 = 12. Value of 1 part = 156/12 = 13. A's share = 5 x 13 = Rs. 65.
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Question 36 of 100
The income and expenditure of a person are in the ratio 9:8. If his income is Rs. 5346, find his savings.
ExplanationLet income = 9x, expenditure = 8x. Given 9x = 5346 => x = 594. Expenditure = 8 x 594 = 4752. Savings = Income - Expenditure = 5346 - 4752 = Rs. 594.
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Question 37 of 100
Two numbers are in the ratio 9:2. If their difference is 70, find the larger number.
ExplanationLet numbers be 9x and 2x. Difference = (9-2)x = 70 => x = 10. Larger number = 9 x 10 = 90.
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Question 38 of 100
Simplify the ratio 112:168 to its lowest terms.
ExplanationHCF of 112 and 168 is 56. Dividing both terms: 112/56 : 168/56 = 2:3.
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Question 39 of 100
In a class, the ratio of boys to girls is 7:8. If the total number of students is 195, find the number of girls.
ExplanationTotal parts = 7+8 = 15. Value of 1 part = 195/15 = 13. Number of girls = 8 x 13 = 104.
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Question 40 of 100
A sum of Rs. 72 is divided among P, Q and R in the ratio 2:4:3. What is Q's share?
ExplanationTotal parts = 2+4+3 = 9. Value of 1 part = 72/9 = 8. Q's share = 4 x 8 = Rs. 32.
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Question 41 of 100
If A:B = 8:9 and A = 136, find the value of B.
ExplanationSince A:B = 8:9, B = A x (9/8) = 136 x 9/8 = 153.
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Question 42 of 100
Simplify the ratio 120:110 to its lowest terms.
ExplanationHCF of 120 and 110 is 10. Dividing both terms: 120/10 : 110/10 = 12:11.
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Question 43 of 100
A sum of Rs. 120 is divided among P, Q and R in the ratio 3:4:5. What is Q's share?
ExplanationTotal parts = 3+4+5 = 12. Value of 1 part = 120/12 = 10. Q's share = 4 x 10 = Rs. 40.
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Question 44 of 100
In a class, the ratio of boys to girls is 4:7. If the total number of students is 77, find the number of girls.
ExplanationTotal parts = 4+7 = 11. Value of 1 part = 77/11 = 7. Number of girls = 7 x 7 = 49.
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Question 45 of 100
The income and expenditure of a person are in the ratio 4:3. If his income is Rs. 7348, find his savings.
ExplanationLet income = 4x, expenditure = 3x. Given 4x = 7348 => x = 1837. Expenditure = 3 x 1837 = 5511. Savings = Income - Expenditure = 7348 - 5511 = Rs. 1837.
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Question 46 of 100
The income and expenditure of a person are in the ratio 9:5. If his income is Rs. 8343, find his savings.
ExplanationLet income = 9x, expenditure = 5x. Given 9x = 8343 => x = 927. Expenditure = 5 x 927 = 4635. Savings = Income - Expenditure = 8343 - 4635 = Rs. 3708.
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Question 47 of 100
If A:B = 3:2 and A = 24, find the value of B.
ExplanationSince A:B = 3:2, B = A x (2/3) = 24 x 2/3 = 16.
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Question 48 of 100
A sum of Rs. 286 is divided among P, Q and R in the ratio 5:6:2. What is Q's share?
ExplanationTotal parts = 5+6+2 = 13. Value of 1 part = 286/13 = 22. Q's share = 6 x 22 = Rs. 132.
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Question 49 of 100
Divide Rs. 87 between A and B in the ratio 1:2. What is A's share?
ExplanationTotal parts = 1+2 = 3. Value of 1 part = 87/3 = 29. A's share = 1 x 29 = Rs. 29.
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Question 50 of 100
If 5:10 :: 9:x, find the value of x.
ExplanationIn a proportion, product of extremes = product of means: 5 x x = 10 x 9 => x = 90/5 = 18.
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Question 51 of 100
Simplify the ratio 14:10 to its lowest terms.
ExplanationHCF of 14 and 10 is 2. Dividing both terms: 14/2 : 10/2 = 7:5.
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Question 52 of 100
In a factory, the ratio of male to female workers is 5:9. If there are 135 male workers, how many female workers are there?
ExplanationSince male:female = 5:9, and male = 135, one part = 135/5 = 27. Female workers = 9 x 27 = 243.
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Question 53 of 100
Which ratio is greater: 3:8 or 4:9?
Explanation3:8 = 0.375, 4:9 = 0.444. Since 0.444 > 0.375, the greater ratio is 4:9.
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Question 54 of 100
A sum of Rs. 144 is divided among P, Q and R in the ratio 3:4:1. What is Q's share?
ExplanationTotal parts = 3+4+1 = 8. Value of 1 part = 144/8 = 18. Q's share = 4 x 18 = Rs. 72.
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Question 55 of 100
The ages of two persons are in the ratio 7:5. If the sum of their ages is 132 years, find the age of the elder person.
ExplanationLet ages be 7x and 5x. Sum = 12x = 132 => x = 11. Elder's age = 7 x 11 = 77 years.
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Question 56 of 100
Two cars cover the same distance in the ratio of times 2:7. What is the ratio of their speeds?
ExplanationFor the same distance, speed is inversely proportional to time. So speed ratio = 7:2 (inverse of time ratio 2:7), simplified = 7:2.
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Question 57 of 100
Divide Rs. 143 between A and B in the ratio 6:5. What is A's share?
ExplanationTotal parts = 6+5 = 11. Value of 1 part = 143/11 = 13. A's share = 6 x 13 = Rs. 78.
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Question 58 of 100
If A:B = 3:4 and B:C = 5:4, find A:B:C.
ExplanationLCM of B-values (4 and 5) = 20. Scale A:B = 15:20 and B:C = 20:16. So A:B:C = 15:20:16 (in lowest terms).
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Question 59 of 100
If A:B = 3:4 and B:C = 5:6, find A:B:C.
ExplanationLCM of B-values (4 and 5) = 20. Scale A:B = 15:20 and B:C = 20:24. So A:B:C = 15:20:24 (in lowest terms).
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Question 60 of 100
Divide Rs. 70 between A and B in the ratio 1:9. What is A's share?
ExplanationTotal parts = 1+9 = 10. Value of 1 part = 70/10 = 7. A's share = 1 x 7 = Rs. 7.
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Question 61 of 100
Simplify the ratio 60:25 to its lowest terms.
ExplanationHCF of 60 and 25 is 5. Dividing both terms: 60/5 : 25/5 = 12:5.
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Question 62 of 100
In a class, the ratio of boys to girls is 4:7. If the total number of students is 242, find the number of girls.
ExplanationTotal parts = 4+7 = 11. Value of 1 part = 242/11 = 22. Number of girls = 7 x 22 = 154.
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Question 63 of 100
Simplify the ratio 50:60 to its lowest terms.
ExplanationHCF of 50 and 60 is 10. Dividing both terms: 50/10 : 60/10 = 5:6.
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Question 64 of 100
Which ratio is greater: 7:9 or 8:11?
Explanation7:9 = 0.778, 8:11 = 0.727. Since 0.778 > 0.727, the greater ratio is 7:9.
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Question 65 of 100
The ages of two persons are in the ratio 2:3. If the sum of their ages is 50 years, find the age of the elder person.
ExplanationLet ages be 2x and 3x. Sum = 5x = 50 => x = 10. Elder's age = 3 x 10 = 30 years.
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Question 66 of 100
Two numbers are in the ratio 5:4. If their difference is 14, find the larger number.
ExplanationLet numbers be 5x and 4x. Difference = (5-4)x = 14 => x = 14. Larger number = 5 x 14 = 70.
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Question 67 of 100
If A:B = 3:5 and A = 30, find the value of B.
ExplanationSince A:B = 3:5, B = A x (5/3) = 30 x 5/3 = 50.
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Question 68 of 100
Two numbers are in the ratio 7:6. If their difference is 16, find the larger number.
ExplanationLet numbers be 7x and 6x. Difference = (7-6)x = 16 => x = 16. Larger number = 7 x 16 = 112.
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Question 69 of 100
The ages of two persons are in the ratio 6:5. If the sum of their ages is 77 years, find the age of the elder person.
ExplanationLet ages be 6x and 5x. Sum = 11x = 77 => x = 7. Elder's age = 6 x 7 = 42 years.
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Question 70 of 100
If A:B = 2:7 and A = 18, find the value of B.
ExplanationSince A:B = 2:7, B = A x (7/2) = 18 x 7/2 = 63.
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Question 71 of 100
The ages of two persons are in the ratio 4:7. If the sum of their ages is 88 years, find the age of the elder person.
ExplanationLet ages be 4x and 7x. Sum = 11x = 88 => x = 8. Elder's age = 7 x 8 = 56 years.
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Question 72 of 100
Divide Rs. 126 between A and B in the ratio 9:5. What is A's share?
ExplanationTotal parts = 9+5 = 14. Value of 1 part = 126/14 = 9. A's share = 9 x 9 = Rs. 81.
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Question 73 of 100
Find the mean proportional between 3 and 12.
ExplanationMean proportional = sqrt(3 x 12) = sqrt(36) = 6.
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Question 74 of 100
Two numbers are in the ratio 7:3. If their difference is 68, find the larger number.
ExplanationLet numbers be 7x and 3x. Difference = (7-3)x = 68 => x = 17. Larger number = 7 x 17 = 119.
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Question 75 of 100
The ages of two persons are in the ratio 5:4. If the sum of their ages is 54 years, find the age of the elder person.
ExplanationLet ages be 5x and 4x. Sum = 9x = 54 => x = 6. Elder's age = 5 x 6 = 30 years.
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Question 76 of 100
In a class, the ratio of boys to girls is 5:3. If the total number of students is 160, find the number of girls.
ExplanationTotal parts = 5+3 = 8. Value of 1 part = 160/8 = 20. Number of girls = 3 x 20 = 60.
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Question 77 of 100
In a factory, the ratio of male to female workers is 7:3. If there are 168 male workers, how many female workers are there?
ExplanationSince male:female = 7:3, and male = 168, one part = 168/7 = 24. Female workers = 3 x 24 = 72.
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Question 78 of 100
Simplify the ratio 25:45 to its lowest terms.
ExplanationHCF of 25 and 45 is 5. Dividing both terms: 25/5 : 45/5 = 5:9.
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Question 79 of 100
Simplify the ratio 77:33 to its lowest terms.
ExplanationHCF of 77 and 33 is 11. Dividing both terms: 77/11 : 33/11 = 7:3.
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Question 80 of 100
The income and expenditure of a person are in the ratio 8:5. If his income is Rs. 22168, find his savings.
ExplanationLet income = 8x, expenditure = 5x. Given 8x = 22168 => x = 2771. Expenditure = 5 x 2771 = 13855. Savings = Income - Expenditure = 22168 - 13855 = Rs. 8313.
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Question 81 of 100
Two numbers are in the ratio 5:4. If their difference is 16, find the larger number.
ExplanationLet numbers be 5x and 4x. Difference = (5-4)x = 16 => x = 16. Larger number = 5 x 16 = 80.
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Question 82 of 100
Which ratio is greater: 5:8 or 7:10?
Explanation5:8 = 0.625, 7:10 = 0.700. Since 0.700 > 0.625, the greater ratio is 7:10.
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Question 83 of 100
The income and expenditure of a person are in the ratio 7:4. If his income is Rs. 15421, find his savings.
ExplanationLet income = 7x, expenditure = 4x. Given 7x = 15421 => x = 2203. Expenditure = 4 x 2203 = 8812. Savings = Income - Expenditure = 15421 - 8812 = Rs. 6609.
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Question 84 of 100
The ages of two persons are in the ratio 5:7. If the sum of their ages is 132 years, find the age of the elder person.
ExplanationLet ages be 5x and 7x. Sum = 12x = 132 => x = 11. Elder's age = 7 x 11 = 77 years.
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Question 85 of 100
The ages of two persons are in the ratio 4:3. If the sum of their ages is 42 years, find the age of the elder person.
ExplanationLet ages be 4x and 3x. Sum = 7x = 42 => x = 6. Elder's age = 4 x 6 = 24 years.
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Question 86 of 100
Divide Rs. 270 between A and B in the ratio 5:4. What is A's share?
ExplanationTotal parts = 5+4 = 9. Value of 1 part = 270/9 = 30. A's share = 5 x 30 = Rs. 150.
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Question 87 of 100
Simplify the ratio 35:77 to its lowest terms.
ExplanationHCF of 35 and 77 is 7. Dividing both terms: 35/7 : 77/7 = 5:11.
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Question 88 of 100
Two cars cover the same distance in the ratio of times 8:7. What is the ratio of their speeds?
ExplanationFor the same distance, speed is inversely proportional to time. So speed ratio = 7:8 (inverse of time ratio 8:7), simplified = 7:8.
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Question 89 of 100
Simplify the ratio 21:12 to its lowest terms.
ExplanationHCF of 21 and 12 is 3. Dividing both terms: 21/3 : 12/3 = 7:4.
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Question 90 of 100
If A:B = 4:9 and A = 44, find the value of B.
ExplanationSince A:B = 4:9, B = A x (9/4) = 44 x 9/4 = 99.
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Question 91 of 100
If A:B = 7:3 and A = 105, find the value of B.
ExplanationSince A:B = 7:3, B = A x (3/7) = 105 x 3/7 = 45.
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Question 92 of 100
Divide Rs. 208 between A and B in the ratio 7:6. What is A's share?
ExplanationTotal parts = 7+6 = 13. Value of 1 part = 208/13 = 16. A's share = 7 x 16 = Rs. 112.
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Question 93 of 100
A sum of Rs. 70 is divided among P, Q and R in the ratio 2:3:5. What is Q's share?
ExplanationTotal parts = 2+3+5 = 10. Value of 1 part = 70/10 = 7. Q's share = 3 x 7 = Rs. 21.
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Question 94 of 100
If A:B = 3:2 and A = 33, find the value of B.
ExplanationSince A:B = 3:2, B = A x (2/3) = 33 x 2/3 = 22.
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Question 95 of 100
Which ratio is greater: 2:3 or 4:5?
Explanation2:3 = 0.667, 4:5 = 0.800. Since 0.800 > 0.667, the greater ratio is 4:5.
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Question 96 of 100
Divide Rs. 144 between A and B in the ratio 7:9. What is A's share?
ExplanationTotal parts = 7+9 = 16. Value of 1 part = 144/16 = 9. A's share = 7 x 9 = Rs. 63.
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Question 97 of 100
Simplify the ratio 28:48 to its lowest terms.
ExplanationHCF of 28 and 48 is 4. Dividing both terms: 28/4 : 48/4 = 7:12.
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Question 98 of 100
Divide Rs. 208 between A and B in the ratio 9:7. What is A's share?
ExplanationTotal parts = 9+7 = 16. Value of 1 part = 208/16 = 13. A's share = 9 x 13 = Rs. 117.
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Question 99 of 100
If A:B = 7:2 and A = 119, find the value of B.
ExplanationSince A:B = 7:2, B = A x (2/7) = 119 x 2/7 = 34.
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Question 100 of 100
The ages of two persons are in the ratio 6:5. If the sum of their ages is 44 years, find the age of the elder person.
ExplanationLet ages be 6x and 5x. Sum = 11x = 44 => x = 4. Elder's age = 6 x 4 = 24 years.
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