Click on a question to see the answer and explanation.
▶1. What is the ratio of 8 to 12?
Answer: 2:3
Explanation: Divide both numbers by their greatest common divisor (4): 8 ÷ 4 = 2, 12 ÷ 4 = 3. So, the ratio is 2:3.
▶2. If the ratio of boys to girls in a class is 3:5 and there are 15 boys, how many girls are there?
Answer: 25
Explanation: 3 parts = 15 boys, so 1 part = 5. Girls = 5 parts = 5 × 5 = 25.
▶3. Simplify the ratio 45:60.
Answer: 3:4
Explanation: Divide both by 15: 45 ÷ 15 = 3, 60 ÷ 15 = 4. So, 3:4.
▶4. If 2:3 = x:12, find x.
Answer: 8
Explanation: 2/3 = x/12 ⇒ x = (2 × 12)/3 = 24/3 = 8.
▶5. Divide 90 in the ratio 2:7.
Answer: 20 and 70
Explanation: Total parts = 2 + 7 = 9. First part = (2/9) × 90 = 20. Second part = (7/9) × 90 = 70.
▶6. If a:b = 4:5 and b:c = 2:3, find a:b:c.
Answer: 8:10:15
Explanation: Make b the same in both ratios: a:b = 4:5, b:c = 2:3. LCM of 5 and 2 is 10. So, a:b = 8:10, b:c = 10:15. So, a:b:c = 8:10:15.
▶7. What is the fourth proportional to 2, 6, 8?
Answer: 24
Explanation: Fourth proportional x = (6 × 8)/2 = 48/2 = 24.
▶8. If 5:7 = 15:x, find x.
Answer: 21
Explanation: 5/7 = 15/x ⇒ x = (7 × 15)/5 = 21.
▶9. If the ratio of ages of A and B is 3:4 and A is 18, what is B's age?
Answer: 24
Explanation: 3 parts = 18, so 1 part = 6. B = 4 parts = 4 × 6 = 24.
▶10. If x:y = 7:9 and y:z = 3:5, find x:y:z.
Answer: 21:27:45
Explanation: Make y the same: x:y = 7:9, y:z = 3:5. LCM of 9 and 3 is 9. x:y = 7:9, y:z = 9:15. So, x:y:z = 21:27:45.
▶11. If 3x = 4y, what is x:y?
Answer: 4:3
Explanation: 3x = 4y ⇒ x/y = 4/3. So, x:y = 4:3.
▶12. If a:b = 2:5, b:c = 3:4, find a:b:c.
Answer: 6:15:20
Explanation: Make b the same: a:b = 2:5, b:c = 3:4. LCM of 5 and 3 is 15. a:b = 6:15, b:c = 15:20. So, a:b:c = 6:15:20.
▶13. If 2:3 = 4:x, find x.
Answer: 6
Explanation: 2/3 = 4/x ⇒ x = (3 × 4)/2 = 6.
▶14. If the ratio of two numbers is 5:8 and their sum is 65, find the numbers.
Answer: 25 and 40
Explanation: Total parts = 5 + 8 = 13. Each part = 65/13 = 5. Numbers: 5 × 5 = 25, 8 × 5 = 40.
▶15. If a:b = 3:4 and b:c = 5:6, find a:b:c.
Answer: 15:20:24
Explanation: Make b the same: a:b = 3:4, b:c = 5:6. LCM of 4 and 5 is 20. a:b = 15:20, b:c = 20:24. So, a:b:c = 15:20:24.
▶16. If 5:7 = x:21, find x.
Answer: 15
Explanation: 5/7 = x/21 ⇒ x = (5 × 21)/7 = 15.
▶17. If 2x = 3y, what is x:y?
Answer: 3:2
Explanation: 2x = 3y ⇒ x/y = 3/2. So, x:y = 3:2.
▶18. If the ratio of two numbers is 7:9 and their difference is 8, find the numbers.
Answer: 28 and 36
Explanation: Difference in ratio = 9 - 7 = 2. Each part = 8/2 = 4. Numbers: 7 × 4 = 28, 9 × 4 = 36.
▶19. If a:b = 2:3 and b:c = 4:5, find a:b:c.
Answer: 8:12:15
Explanation: Make b the same: a:b = 2:3, b:c = 4:5. LCM of 3 and 4 is 12. a:b = 8:12, b:c = 12:15. So, a:b:c = 8:12:15.
▶20. If 3:4 = x:20, find x.
Answer: 15
Explanation: 3/4 = x/20 ⇒ x = (3 × 20)/4 = 15.