RATIO AND PROPORTIONS

Ratios and Proportions - Tough Revision Questions

1. Simplify the ratio 84:126:168.
2. A recipe uses flour, sugar, and butter in the ratio 4:2:1. How much of each is needed to make 7 kg of mixture?
3. The ratio of boys to girls in a school is 7:9. If there are 432 girls, how many boys are there?
4. If 5 pens cost TZS 3500, how much would 13 pens cost at the same rate?
5. A mixture contains water and juice in the ratio 5:3. How many liters of juice are in 64 liters of mixture?
6. Divide TZS 84,000 in the ratio 4:7.
7. The scale on a map is 1:50,000. What is the real distance (in km) for 7.5 cm on the map?
8. The angles in a triangle are in the ratio 2:3:4. Find the measure of each angle.
9. If a:b = 3:5 and b:c = 2:7, find the ratio a:c.
10. A car travels 210 km using 14 liters of petrol. How much petrol will it use for 525 km?
11. A and B divide a profit in the ratio 3:4. If the total profit is TZS 280,000, how much does each get?
12. If x:y = 2:3 and y:z = 4:5, find the value of x:z.
13. In what ratio should TZS 12,000 be divided so that the first part is twice the second?
14. The ratio of red to blue marbles is 5:2. If there are 84 marbles in total, how many are red?
15. Two numbers are in the ratio 7:11. If their sum is 360, find the numbers.
16. The sides of two similar triangles are in the ratio 3:5. If the smaller triangle has an area of 54 cm², find the area of the larger triangle.
17. The weights of three people are in the ratio 8:9:10. If the heaviest weighs 90 kg, find the lightest.
18. If 4 workers can complete a job in 6 days, how many days will 6 workers take to complete the same job (assuming equal efficiency)?
19. Divide 275 in the ratio 3:5:7.
20. If the ratio of angles in a quadrilateral is 2:3:3:4, find the measure of each angle.
21. A rope is cut in the ratio 2:3:5. If the longest piece is 10 m, find the total length of the rope.
22. Two numbers are in the ratio 4:9. If their difference is 75, find the numbers.
23. The ratio of the number of boys to the number of girls is 5:6. If there are 440 students in total, how many are girls?
24. If 3 bags of rice feed 12 people for 5 days, how many bags are needed to feed 20 people for 10 days?
25. In what ratio must water be added to 80 mL of acid to get a 20% acid solution?
26. The price of 3 kg of beans is TZS 6,750. What is the cost of 8.5 kg?
27. A 60 m pipe is cut into parts in the ratio 5:4. What is the length of each part?
28. A: B = 2:5, B: C = 3:4. Find A:B:C.
29. Three partners share a profit of TZS 1,020,000 in the ratio 5:3:2. How much does each receive?
30. A liquid is made by mixing alcohol and water in the ratio 3:7. How much alcohol is there in 2.5 L of the mixture?