Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 584 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 28 days (d) 11 days
2. 2.₹325 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹200 (b) ₹225 (c) ₹125 (d) ₹25
3. 3.If 3 kites cost ₹66, how much do 9 kites cost? (a) ₹594 (b) ₹198 (c) ₹72 (d) ₹220
4. 4.If 3 pens cost ₹24, how much do 9 pens cost? (a) ₹80 (b) ₹30 (c) ₹72 (d) ₹216
5. 5.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 19 days (c) 18 days (d) 2 days
6. 6.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 1 day (d) 8 days
7. 7.If 4 mangoes cost ₹40, how much do 5 mangoes cost? (a) ₹41 (b) ₹60 (c) ₹200 (d) ₹50
8. 8.If 8 kites cost ₹56, how much do 11 kites cost? (a) ₹59 (b) ₹616 (c) ₹77 (d) ₹84
9. 9.₹130 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹13 (b) ₹65 (c) ₹91 (d) ₹39
10. 10.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 19 days (d) 49 days
11. 11.₹72 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹30 (b) ₹36 (c) ₹6 (d) ₹42
12. 12.₹533 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹205 (b) ₹328 (c) ₹369 (d) ₹41
13. 13.If 6 mangoes cost ₹120, how much do 7 mangoes cost? (a) ₹140 (b) ₹840 (c) ₹160 (d) ₹121
14. 14.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 2 days (d) 15 days
15. 15.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 29 days (c) 3 days (d) 13 days
16. 16.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 34 days (b) 5 days (c) 33 days (d) 17 days
17. 17.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 14 days (c) 8 days (d) 9 days
18. 18.₹78 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹6 (b) ₹24 (c) ₹54 (d) ₹39
19. 19.₹215 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹43 (b) ₹172 (c) ₹173 (d) ₹215
20. 20.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 18 days (d) 19 days
21. 21.₹308 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹88 (b) ₹44 (c) ₹220 (d) ₹154
22. 22.₹69 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹69 (b) ₹46 (c) ₹23 (d) ₹47
23. 23.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 8 days (d) 7 days
24. 24.If 6 kites cost ₹96, how much do 4 kites cost? (a) ₹94 (b) ₹80 (c) ₹384 (d) ₹64
25. 25.If 8 pens cost ₹120, how much do 9 pens cost? (a) ₹150 (b) ₹1080 (c) ₹135 (d) ₹121
26. 26.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 20 days (d) 5 days
27. 27.₹52 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹26 (b) ₹52 (c) ₹39 (d) ₹13
28. 28.₹30 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹15 (b) ₹6 (c) ₹30 (d) ₹24
29. 29.If 6 mangoes cost ₹48, how much do 2 mangoes cost? (a) ₹96 (b) ₹24 (c) ₹44 (d) ₹16
30. 30.₹264 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹132 (b) ₹165 (c) ₹33 (d) ₹99
31. 31.If 3 pens cost ₹27, how much do 4 pens cost? (a) ₹28 (b) ₹108 (c) ₹36 (d) ₹45
32. 32.₹476 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹238 (b) ₹34 (c) ₹306 (d) ₹170
33. 33.₹143 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹99 (b) ₹55 (c) ₹11 (d) ₹88
34. 34.If 4 kites cost ₹40, how much do 12 kites cost? (a) ₹120 (b) ₹480 (c) ₹48 (d) ₹130
35. 35.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 13 days (d) 25 days
36. 36.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 15 days
37. 37.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 11 days (d) 26 days
38. 38.₹198 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹198 (b) ₹99 (c) ₹176 (d) ₹22
39. 39.If 4 kites cost ₹24, how much do 6 kites cost? (a) ₹42 (b) ₹36 (c) ₹144 (d) ₹26
40. 40.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 10 days (d) 7 days

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