Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 365 · 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. 1.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 14 days (c) 30 days (d) 31 days
2. 2.If 8 mangoes cost ₹96, how much do 9 mangoes cost? (a) ₹120 (b) ₹864 (c) ₹108 (d) ₹97
3. 3.If 4 pens cost ₹20, how much do 9 pens cost? (a) ₹25 (b) ₹45 (c) ₹50 (d) ₹180
4. 4.₹207 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹23 (b) ₹138 (c) ₹92 (d) ₹115
5. 5.If 6 pens cost ₹138, how much do 7 pens cost? (a) ₹139 (b) ₹966 (c) ₹184 (d) ₹161
6. 6.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 10 days (d) 12 days
7. 7.₹264 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹132 (b) ₹22 (c) ₹110 (d) ₹154
8. 8.₹140 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹70 (b) ₹14 (c) ₹98 (d) ₹42
9. 9.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 1 day
10. 10.₹185 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹37 (b) ₹111 (c) ₹74 (d) ₹148
11. 11.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 3 days (d) 4 days
12. 12.If 2 pens cost ₹36, how much do 7 pens cost? (a) ₹126 (b) ₹252 (c) ₹144 (d) ₹41
13. 13.₹180 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹72 (b) ₹36 (c) ₹90 (d) ₹108
14. 14.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 5 days (d) 6 days
15. 15.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 42 days (b) 10 days (c) 18 days (d) 43 days
16. 16.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹15 (b) ₹90 (c) ₹105 (d) ₹75
17. 17.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 1 day (d) 3 days
18. 18.₹120 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹12 (b) ₹60 (c) ₹108 (d) ₹120
19. 19.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 9 days (d) 7 days
20. 20.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 4 days (d) 18 days
21. 21.₹630 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹225 (b) ₹45 (c) ₹315 (d) ₹405
22. 22.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 61 days (b) 9 days (c) 60 days (d) 21 days
23. 23.If 4 pens cost ₹60, how much do 8 pens cost? (a) ₹64 (b) ₹120 (c) ₹135 (d) ₹480
24. 24.If 4 notebooks cost ₹56, how much do 8 notebooks cost? (a) ₹60 (b) ₹126 (c) ₹112 (d) ₹448
25. 25.If 2 mangoes cost ₹18, how much do 8 mangoes cost? (a) ₹24 (b) ₹144 (c) ₹81 (d) ₹72
26. 26.₹168 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹21 (b) ₹84 (c) ₹105 (d) ₹63
27. 27.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 9 days (d) 4 days
28. 28.If 3 pens cost ₹15, how much do 6 pens cost? (a) ₹90 (b) ₹18 (c) ₹35 (d) ₹30
29. 29.₹368 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹46 (b) ₹138 (c) ₹230 (d) ₹184
30. 30.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 21 days (d) 45 days
31. 31.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 6 days (d) 4 days
32. 32.₹585 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹450 (b) ₹180 (c) ₹45 (d) ₹405
33. 33.If 9 mangoes cost ₹198, how much do 10 mangoes cost? (a) ₹242 (b) ₹1980 (c) ₹199 (d) ₹220
34. 34.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 3 days (c) 22 days (d) 11 days
35. 35.₹410 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹205 (b) ₹123 (c) ₹287 (d) ₹41
36. 36.8 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 24 days (c) 14 days (d) 25 days
37. 37.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹10 (b) ₹25 (c) ₹40 (d) ₹50
38. 38.If 8 mangoes cost ₹200, how much do 3 mangoes cost? (a) ₹100 (b) ₹75 (c) ₹195 (d) ₹600
39. 39.If 7 kites cost ₹49, how much do 6 kites cost? (a) ₹49 (b) ₹294 (c) ₹42 (d) ₹48
40. 40.If 3 kites cost ₹30, how much do 7 kites cost? (a) ₹210 (b) ₹80 (c) ₹34 (d) ₹70

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