Ratio and Proportion Practice Questions

1. Write the ratio of 48 cm to 2 m in the simplest form.
2. The ratio of boys to girls in a class is 7 : 9. If there are 144 students, find the number of boys and girls.
3. Divide ₹18,000 among A, B and C in the ratio 2 : 3 : 5.
4. The ratio of milk and water in a mixture is 5 : 3. If the mixture contains 64 litres, find the quantity of milk and water.
5. The present ages of a father and son are in the ratio 9 : 2. If the father is 45 years old, find the son’s age.
6. Find x if 8 : 12 = x : 30.
7. The length and breadth of a rectangle are in the ratio 7 : 4. If the perimeter is 110 cm, find its dimensions.
8. Simplify the ratio 3/4 : 5/6.
9. Two numbers are in the ratio 8 : 11. If their sum is 228, find the numbers.
10. A map is drawn to the scale 1 : 25,000. If the distance between two villages on the map is 8 cm, find the actual distance.
11. A recipe requires rice and pulses in the ratio 4 : 1. If 30 kg of rice is used, how much pulses are required?
12. Express 2.5 kg : 750 g in the simplest form.
13. The ratio of the sides of two squares is 3 : 5. If the smaller square has a side of 18 cm, find the side of the larger square.
14. Divide ₹24,500 between A and B in the ratio 7 : 3.
15. A car travels 180 km using 12 litres of petrol. How much petrol is needed to travel 330 km?
16. The ratio of English books to Hindi books is 8 : 5. If there are 104 books altogether, find the number of each type.
17. The ratio of two numbers is 5 : 9. If their difference is 32, find the numbers.
18. Find the fourth proportional to 6, 9 and 15.
19. A tank contains petrol and diesel in the ratio 7 : 5. If the total fuel is 180 litres, find the quantity of each.
20. Two numbers are in the ratio 4 : 7. If their HCF is 9, find the numbers.
21. The ratio of the present ages of two sisters is 5 : 8. Their total age is 52 years. Find their present ages.
22. A shopkeeper mixes two varieties of tea in the ratio 3 : 5. If he prepares 80 kg of the mixture, find the quantity of each variety.
23. Simplify the ratio 2/5 : 3/10 : 1/2.
24. The ratio of red, blue and green balls is 4 : 5 : 6. If there are 180 balls, find the number of each colour.
25. Find the ratio of 3.5 m to 175 cm.
26. The ratio of income to expenditure is 11 : 8. If the monthly saving is ₹12,000, find the monthly income.
27. A train travels 240 km in 4 hours. How far will it travel in 7 hours at the same speed?
28. The ratio of the areas of two squares is 25 : 49. Find the ratio of their sides.
29. Find x if 4/5 : 2/3 = x : 18.
30. A farmer grows wheat and rice in the ratio 5 : 7. If the total land is 96 hectares, find the area under each crop.
31. Two numbers are in the ratio 6 : 11. If 10 is added to each number, the ratio becomes 8 : 13. Find the numbers.
32. The ratio of boys to girls is 5 : 6. If 12 girls leave the class, the ratio becomes 1 : 1. Find the original number of boys and girls.
33. A rope is divided into three parts in the ratio 2 : 5 : 8. If the longest part is 64 m, find the total length of the rope.
34. Divide ₹42,000 among P, Q and R in the ratio 5 : 7 : 9.
35. The ratio of the speeds of two buses is 4 : 7. If the faster bus runs at 84 km/h, find the speed of the slower bus.
36. The ratio of sugar to flour is 2 : 9. If 18 kg of sugar is used, find the quantity of flour.
37. Express 45 minutes : 2 hours in the simplest form.
38. The ratio of two numbers is 7 : 12. If their sum is 380, find the numbers.
39. The ratio of the sides of two cubes is 2 : 5. Find the ratio of their volumes.
40. A library has Science, Maths and English books in the ratio 6 : 5 : 4. If there are 180 books, find the number of books in each subject.
41. Simplify 5/8 : 15/16.
42. A tank contains 350 litres of water. The ratio of water used to water left is 3 : 4. Find the quantity of water left.
43. A cyclist covers 84 km in 4 hours. How far will he travel in 9 hours at the same speed?
44. Find the ratio of 0.75 litre to 250 mL.
45. The ratio of the radii of two circles is 5 : 8. Find the ratio of their circumferences.
46. The ratio of the monthly salaries of A and B is 7 : 9. If B earns ₹54,000, find A’s salary.
47. The ratio of apples, oranges and mangoes is 5 : 3 : 2. If there are 150 fruits, find the number of each fruit.
48. Find the fourth proportional to 8, 20 and 50.
49. A wall can be painted by 12 workers in 15 days. How many workers are needed to complete the work in 10 days?
50. The ratio of the present ages of a mother and daughter is 11 : 4. If the mother is 44 years old, find the daughter’s age.
51. Divide ₹36,000 between A and B in the ratio 11 : 7.
52. The ratio of two numbers is 9 : 13. If their difference is 20, find the numbers.
53. A map uses the scale 1 : 50,000. If two places are 14 cm apart on the map, find the actual distance.
54. The ratio of milk, water and juice is 6 : 3 : 1. If the mixture is 120 litres, find the quantity of each liquid.
55. Find the simplest ratio of 1.5 : 2.25.
56. A recipe for 8 people requires 600 g of rice. How much rice is needed for 18 people?
57. The ratio of the areas of two rectangles is 4 : 9. If their lengths are in the ratio 2 : 3, find the ratio of their breadths.
58. Two numbers are in the ratio 5 : 8. If their LCM is 240, find the numbers.
59. The population of two villages is in the ratio 7 : 9. If their total population is 8,000, find the population of each village.
60. The ratio of students who passed to those who failed is 13 : 2. If 24 students failed, find the total number of students.
61. The ratio of two numbers is 7 : 9. If 12 is added to each number, the ratio becomes 5 : 6. Find the numbers.
62. The present ages of a father and his son are in the ratio 8 : 3. After 10 years, their ages will be in the ratio 13 : 8. Find their present ages.
63. A milkman mixes milk and water in the ratio 5 : 2. He adds 12 litres of water, and the ratio becomes 5 : 3. Find the original quantity of the mixture.
64. Divide ₹48,000 among A, B and C in the ratio 3 : 5 : 8. If C gives ₹2,000 to A, what will be the new ratio of their amounts?
65. The length and breadth of a rectangle are in the ratio 7 : 4. If its area is 1,008 cm², find its dimensions.
66. Two numbers are in the ratio 5 : 8. Their HCF is 9. Find the numbers and their LCM.
67. The ratio of the radii of two circles is 4 : 7. If the circumference of the larger circle is 132 cm, find the circumference of the smaller circle.
68. The ratio of the areas of two squares is 81 : 121. If the side of the larger square is 44 cm, find the side of the smaller square.
69. A map is drawn to the scale 1 : 40,000. Two villages are 12.5 cm apart on the map. Find the actual distance.
70. A recipe uses flour, sugar and butter in the ratio 5 : 3 : 2. If 18 kg of butter is used, find the total weight of the mixture.
71. The ratio of boys to girls is 9 : 11. If 18 girls leave the class, the ratio becomes 3 : 3. Find the original number of boys and girls.
72. A train covers 270 km in 4.5 hours. How far will it travel in 7.5 hours at the same speed?
73. The ratio of two numbers is 11 : 14. Their difference is 27. Find the numbers.
74. Simplify the ratio 3/4 : 5/6 : 7/8.
75. Divide ₹36,000 between A and B in the ratio 2/3 : 5/6.
76. The ratio of the volumes of two cubes is 64 : 125. If the smaller cube has an edge of 16 cm, find the edge of the larger cube.
77. A person spends his income in the ratio 7 : 2 : 1 on food, education and savings. If his monthly income is ₹80,000, find the amount spent on each.
78. The ratio of petrol to diesel in a tank is 7 : 5. If 24 litres of petrol are removed, the ratio becomes 5 : 5. Find the original quantity of petrol and diesel.
79. A rope is divided into three parts in the ratio 2 : 5 : 9. If the shortest part is 8 metres, find the total length of the rope.
80. The ratio of the present ages of three brothers is 3 : 5 : 7. Their total age is 90 years. Find the age of the eldest brother.
81. A school has boys and girls in the ratio 13 : 12. If 25 new girls are admitted, the ratio becomes 13 : 13. Find the original number of students.
82. Two numbers are in the ratio 8 : 15. Their LCM is 840. Find the numbers.
83. The ratio of the sides of two cubes is 5 : 7. Find the ratio of their surface areas.
84. The ratio of English, Hindi and Science books is 4 : 7 : 9. If there are 360 books in total, find the number of Science books.
85. Find x if 5/8 : 15/16 = x : 24.
86. A contractor can complete a project with 24 workers in 15 days. How many workers are needed to complete the same work in 10 days?
87. The ratio of apples to oranges is 7 : 9. If 18 oranges are sold, the ratio becomes 7 : 6. Find the original number of fruits.
88. The ratio of the cost price and selling price of an article is 8 : 11. If the selling price is ₹6,600, find the profit earned.
89. The ratio of the population of two villages is 5 : 8. If the total population is 9,750, find the population of each village.
90. The ratio of passed students to failed students is 17 : 3. If 42 students failed, find the total number of students.