Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 369 · 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. 1.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 14 days (b) 3 days (c) 18 days (d) 2 days
2. 2.₹112 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹40 (b) ₹8 (c) ₹72 (d) ₹56
3. 3.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 1 day (c) 8 days (d) 10 days
4. 4.If 9 pens cost ₹27, how much do 11 pens cost? (a) ₹297 (b) ₹29 (c) ₹36 (d) ₹33
5. 5.₹451 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹41 (b) ₹369 (c) ₹410 (d) ₹82
6. 6.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 7 days (d) 2 days
7. 7.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 19 days (d) 16 days
8. 8.4 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) 26 days (d) 11 days
9. 9.₹196 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹28 (b) ₹56 (c) ₹98 (d) ₹140
10. 10.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 27 days (c) 28 days (d) 19 days
11. 11.₹190 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹76 (b) ₹114 (c) ₹95 (d) ₹38
12. 12.If 3 pens cost ₹42, how much do 2 pens cost? (a) ₹41 (b) ₹28 (c) ₹84 (d) ₹42
13. 13.If 6 notebooks cost ₹132, how much do 5 notebooks cost? (a) ₹132 (b) ₹131 (c) ₹110 (d) ₹660
14. 14.If 5 mangoes cost ₹55, how much do 2 mangoes cost? (a) ₹33 (b) ₹22 (c) ₹52 (d) ₹110
15. 15.₹473 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹43 (b) ₹172 (c) ₹301 (d) ₹344
16. 16.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 1 day (c) 28 days (d) 13 days
17. 17.If 2 pens cost ₹32, how much do 6 pens cost? (a) ₹112 (b) ₹36 (c) ₹192 (d) ₹96
18. 18.₹220 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹20 (b) ₹100 (c) ₹110 (d) ₹120
19. 19.If 9 pens cost ₹36, how much do 7 pens cost? (a) ₹32 (b) ₹28 (c) ₹34 (d) ₹252
20. 20.₹185 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹149 (b) ₹185 (c) ₹148 (d) ₹37
21. 21.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 7 days
22. 22.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 3 days (d) 21 days
23. 23.₹484 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹242 (b) ₹264 (c) ₹220 (d) ₹44
24. 24.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 6 days (d) 20 days
25. 25.₹506 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹253 (b) ₹368 (c) ₹138 (d) ₹46
26. 26.₹350 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹50 (b) ₹250 (c) ₹100 (d) ₹175
27. 27.If 8 pens cost ₹88, how much do 11 pens cost? (a) ₹121 (b) ₹91 (c) ₹132 (d) ₹968
28. 28.4 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) 5 days (d) 8 days
29. 29.If 3 kites cost ₹9, how much do 4 kites cost? (a) ₹36 (b) ₹15 (c) ₹12 (d) ₹10
30. 30.If 5 kites cost ₹30, how much do 6 kites cost? (a) ₹180 (b) ₹31 (c) ₹42 (d) ₹36
31. 31.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 11 days
32. 32.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 28 days (d) 7 days
33. 33.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹24 (b) ₹72 (c) ₹96 (d) ₹120
34. 34.₹64 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹56 (b) ₹64 (c) ₹32 (d) ₹8
35. 35.If 4 notebooks cost ₹76, how much do 2 notebooks cost? (a) ₹57 (b) ₹152 (c) ₹74 (d) ₹38
36. 36.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 23 days (c) 9 days (d) 22 days
37. 37.If 5 kites cost ₹30, how much do 2 kites cost? (a) ₹18 (b) ₹12 (c) ₹27 (d) ₹60
38. 38.If 4 notebooks cost ₹60, how much do 7 notebooks cost? (a) ₹63 (b) ₹120 (c) ₹420 (d) ₹105
39. 39.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 16 days (d) 17 days
40. 40.If 7 notebooks cost ₹161, how much do 9 notebooks cost? (a) ₹207 (b) ₹230 (c) ₹163 (d) ₹1449

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