Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 826 · 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 15 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 11 days (d) 19 days
2. 2.₹77 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹7 (b) ₹63 (c) ₹70 (d) ₹14
3. 3.If 8 pens cost ₹184, how much do 7 pens cost? (a) ₹183 (b) ₹161 (c) ₹1288 (d) ₹184
4. 4.If 4 mangoes cost ₹60, how much do 9 mangoes cost? (a) ₹135 (b) ₹150 (c) ₹540 (d) ₹65
5. 5.If 5 kites cost ₹30, how much do 3 kites cost? (a) ₹90 (b) ₹24 (c) ₹28 (d) ₹18
6. 6.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 1 day (d) 3 days
7. 7.₹308 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹22 (b) ₹154 (c) ₹110 (d) ₹198
8. 8.₹275 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹225 (b) ₹200 (c) ₹75 (d) ₹25
9. 9.If 6 notebooks cost ₹36, how much do 7 notebooks cost? (a) ₹48 (b) ₹252 (c) ₹37 (d) ₹42
10. 10.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 2 days (d) 3 days
11. 11.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 15 days (c) 3 days (d) 27 days
12. 12.₹102 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹34 (b) ₹102 (c) ₹51 (d) ₹68
13. 13.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 63 days (b) 7 days (c) 64 days (d) 21 days
14. 14.₹203 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹29 (b) ₹174 (c) ₹145 (d) ₹58
15. 15.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 14 days (c) 3 days (d) 15 days
16. 16.8 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 18 days (d) 16 days
17. 17.If 3 kites cost ₹75, how much do 11 kites cost? (a) ₹275 (b) ₹83 (c) ₹300 (d) ₹825
18. 18.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 36 days (d) 35 days
19. 19.If 2 kites cost ₹50, how much do 12 kites cost? (a) ₹300 (b) ₹60 (c) ₹325 (d) ₹600
20. 20.If 8 kites cost ₹104, how much do 9 kites cost? (a) ₹936 (b) ₹117 (c) ₹130 (d) ₹105
21. 21.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 18 days (d) 36 days
22. 22.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹84 (b) ₹14 (c) ₹98 (d) ₹70
23. 23.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 31 days (c) 30 days (d) 13 days
24. 24.₹258 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹129 (b) ₹258 (c) ₹215 (d) ₹43
25. 25.If 2 pens cost ₹10, how much do 5 pens cost? (a) ₹13 (b) ₹50 (c) ₹30 (d) ₹25
26. 26.₹126 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹63 (b) ₹105 (c) ₹21 (d) ₹126
27. 27.If 6 kites cost ₹132, how much do 3 kites cost? (a) ₹396 (b) ₹88 (c) ₹66 (d) ₹129
28. 28.₹528 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹48 (b) ₹432 (c) ₹264 (d) ₹96
29. 29.If 5 kites cost ₹50, how much do 3 kites cost? (a) ₹30 (b) ₹48 (c) ₹150 (d) ₹40
30. 30.₹288 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹120 (b) ₹144 (c) ₹24 (d) ₹168
31. 31.6 workers can build a wall in 14 days. How many days will 12 workers take, working at the same speed? (a) 28 days (b) 8 days (c) 20 days (d) 7 days
32. 32.If 4 notebooks cost ₹36, how much do 8 notebooks cost? (a) ₹288 (b) ₹81 (c) ₹40 (d) ₹72
33. 33.If 9 notebooks cost ₹207, how much do 6 notebooks cost? (a) ₹1242 (b) ₹161 (c) ₹138 (d) ₹204
34. 34.₹224 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹28 (b) ₹196 (c) ₹112 (d) ₹224
35. 35.If 3 notebooks cost ₹36, how much do 5 notebooks cost? (a) ₹72 (b) ₹180 (c) ₹38 (d) ₹60
36. 36.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 5 days (d) 9 days
37. 37.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 21 days (c) 22 days (d) 13 days
38. 38.If 3 notebooks cost ₹15, how much do 12 notebooks cost? (a) ₹65 (b) ₹180 (c) ₹60 (d) ₹24
39. 39.If 9 kites cost ₹45, how much do 3 kites cost? (a) ₹39 (b) ₹20 (c) ₹15 (d) ₹135
40. 40.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 17 days (d) 6 days

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