Ratio and proportion problems. - One Line Questions

1. If 0.5 : x = 1.5 : 9, find x. — 3
2. If a:b = 1/2 : 1/3 and b:c = 1/3 : 1/4, find a:c. — 4:1
3. In what ratio does the point (2, 3) divide the line segment joining the points (-1, -2) and (5, 8)? — 1:2
4. The ratio of the areas of two circles is 1:4. What is the ratio of their radii? — 1:2
5. What is the fourth proportional to 4, 6, and 8? — 12
6. The ratio of two numbers is 9:13. If the sum of the numbers is 110, find the difference between the numbers. — 20
7. If the ratio of the number of apples and oranges in a basket is 5:3. If there are 24 fruits in total, how many apples are there? — 15
8. The ratio of two numbers is 2:5. If 5 is added to each number, the ratio becomes 3:7. Find the numbers. — 10 and 25
9. The ratio of milk and water in a container is 5:2. If 5 liters of water are added, the ratio becomes 5:3. Find the initial quantity of milk. — 25 liters
10. The ratio of ages of father and son is 7:2. If the difference of their ages is 30 years, what is the age of the son? — 12 years
11. The ratio of the speeds of two trains is 5:6. If the first train covers a distance of 500 km in 5 hours, what is the speed of the second train? — 120 km/hr
12. What is the mean proportional between 9 and 25? — 15
13. If the ratio of the sides of a rectangle is 3:5 and its perimeter is 80 cm, what is the length of the longer side? — 25 cm
14. In a mixture of milk and water, the ratio of milk to water is 7:3. If the total volume of the mixture is 50 liters, how much milk is there? — 35 liters
15. If 12:18 = x:27, find x. — 18
16. What is the third proportional to 6 and 12? — 24
17. The ratio of the ages of two brothers is 3:4. If the sum of their ages is 42 years, what is the age of the elder brother? — 24 years
18. If a:b = 2:3 and b:c = 4:5, find the ratio a:b:c. — 8:12:15
19. If x/y = 2/3 and y/z = 4/5, find x:z. — 8:15
20. If the ratio of two numbers is 3:5 and their sum is 80, what are the numbers? — 30 and 50
21. The ratio of copper and zinc in an alloy is 3:2. If the weight of the alloy is 50 kg, what is the weight of copper? — 30 kg
22. In what ratio must rice at Rs. 80 per kg be mixed with rice at Rs. 120 per kg so that the mixture is worth Rs. 90 per kg? — 3:1
23. If 2x = 3y = 6z, find the ratio x:y:z. — 3:2:1
24. The ratio of the areas of two squares is 9:16. What is the ratio of their perimeters? — 3:4
25. If 3x = 5y, what is the ratio x:y? — 5:3
26. If a:b = 3:4 and b:c = 5:7, find the ratio a:c. — 15:28
27. The ratio of the number of boys to girls in a group is 5:4. If there are 32 girls, how many boys are there? — 40
28. The ratio of boys to girls in a class is 4:7. If there are 28 boys, how many girls are there? — 49
29. Two numbers are in the ratio 5:8. If the difference between the numbers is 24, find the numbers. — 40 and 64
30. If the ratio of the number of boys and girls in a class is 3:5, and the total number of students is 40, what is the difference between the number of boys and girls? — 10
31. If 4:x = 6:9, find the value of x. — 6
32. The ratio of two numbers is 1:2. If 7 is subtracted from both numbers, the ratio becomes 2:5. Find the numbers. — 9 and 18
33. If a:b = 2:5 and a:c = 4:7, find b:c. — 14:5
34. The ratio of the number of boys and girls in a school is 11:10. If the total number of students is 1260, find the number of girls. — 630
35. If the ratio of angles of a triangle is 1:2:3, what is the measure of the largest angle? — 90 degrees
36. The ratio of two quantities is 7:11. If the first quantity is 49, what is the second quantity? — 77
37. The ratio of the speeds of two cars is 7:9. If the first car travels 210 km in 3 hours, what is the speed of the second car? — 90 km/hr
38. The ratio of the number of male and female employees in a company is 3:2. If there are 150 male employees, how many female employees are there? — 100
39. The ratio of the number of pages in two books is 7:11. If the second book has 132 pages, how many pages does the first book have? — 84
40. Two numbers are in the ratio 3:7. If 8 is added to both numbers, the ratio becomes 5:9. Find the numbers. — 15 and 35
41. The ratio of the ages of Ram and Rahim is 4:5. After 6 years, the ratio of their ages will be 6:7. Find their present ages. — Ram: 16 years, Rahim: 20 years
42. The ratio of the cost of a pen to a pencil is 5:2. If the cost of the pen is Rs. 30, what is the cost of the pencil? — Rs. 12
43. A sum of Rs. 530 is divided among P, Q, and R such that P gets 1/2 of Q and Q gets 1/4 of R. The share of Q is: — Rs. 120
44. A sum of money is divided among A, B, and C in the ratio 2:3:5. If C receives Rs. 500 more than B, what is the total sum of money? — Rs. 2000
45. A sum of Rs. 480 is divided among A, B, and C in the ratio 1/2 : 1/3 : 1/4. The share of B is: — Rs. 192
46. A sum of Rs. 750 is divided among A, B, and C in the ratio 1:2:3. The share of C is: — Rs. 375
47. A sum of money is divided among P, Q, and R in the ratio 3:4:5. If P's share is Rs. 1500, what is R's share? — Rs. 2500
48. The ratio of the prices of two articles is 4:5. If the price of the first article is Rs. 200, what is the price of the second article? — Rs. 250
49. A sum of money is divided between Ram and Shyam in the ratio 4:5. If Ram gets Rs. 400, how much does Shyam get? — Rs. 500
50. The ratio of income to expenditure of a person is 11:10. If he saves Rs. 900 per month, what is his income? — Rs. 9900
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