Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 185 · 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.If 2 notebooks cost ₹34, how much do 9 notebooks cost? (a) ₹153 (b) ₹306 (c) ₹41 (d) ₹170
2. 2.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 16 days (c) 4 days (d) 5 days
3. 3.If 9 notebooks cost ₹90, how much do 10 notebooks cost? (a) ₹110 (b) ₹900 (c) ₹91 (d) ₹100
4. 4.₹276 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹276 (b) ₹46 (c) ₹138 (d) ₹230
5. 5.₹174 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹29 (b) ₹145 (c) ₹174 (d) ₹87
6. 6.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 15 days
7. 7.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 11 days
8. 8.₹90 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹40 (b) ₹45 (c) ₹10 (d) ₹50
9. 9.If 9 pens cost ₹63, how much do 3 pens cost? (a) ₹57 (b) ₹21 (c) ₹189 (d) ₹28
10. 10.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 8 days (b) 18 days (c) 9 days (d) 15 days
11. 11.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 23 days (b) 15 days (c) 22 days (d) 7 days
12. 12.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 10 days (d) 7 days
13. 13.If 6 mangoes cost ₹18, how much do 12 mangoes cost? (a) ₹216 (b) ₹39 (c) ₹24 (d) ₹36
14. 14.₹490 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹245 (b) ₹175 (c) ₹315 (d) ₹35
15. 15.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 24 days (d) 12 days
16. 16.₹126 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹98 (b) ₹63 (c) ₹14 (d) ₹28
17. 17.₹135 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹81 (b) ₹54 (c) ₹108 (d) ₹27
18. 18.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 13 days (d) 17 days
19. 19.₹160 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹100 (b) ₹80 (c) ₹60 (d) ₹20
20. 20.₹370 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹111 (b) ₹259 (c) ₹37 (d) ₹185
21. 21.If 4 pens cost ₹52, how much do 5 pens cost? (a) ₹260 (b) ₹65 (c) ₹78 (d) ₹53
22. 22.₹216 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹108 (b) ₹24 (c) ₹168 (d) ₹48
23. 23.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 49 days (c) 9 days (d) 19 days
24. 24.₹110 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹55 (b) ₹40 (c) ₹70 (d) ₹10
25. 25.If 9 kites cost ₹45, how much do 5 kites cost? (a) ₹25 (b) ₹225 (c) ₹41 (d) ₹30
26. 26.₹54 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹45 (b) ₹27 (c) ₹9 (d) ₹54
27. 27.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 2 days (d) 3 days
28. 28.₹308 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹22 (b) ₹110 (c) ₹154 (d) ₹198
29. 29.₹119 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹85 (b) ₹17 (c) ₹102 (d) ₹34
30. 30.If 8 notebooks cost ₹120, how much do 7 notebooks cost? (a) ₹119 (b) ₹840 (c) ₹120 (d) ₹105
31. 31.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 23 days (c) 45 days (d) 7 days
32. 32.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 10 days (d) 19 days
33. 33.₹120 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹120 (b) ₹40 (c) ₹80 (d) ₹60
34. 34.If 3 pens cost ₹57, how much do 5 pens cost? (a) ₹59 (b) ₹285 (c) ₹114 (d) ₹95
35. 35.If 2 notebooks cost ₹42, how much do 7 notebooks cost? (a) ₹147 (b) ₹168 (c) ₹47 (d) ₹294
36. 36.₹504 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹36 (b) ₹252 (c) ₹324 (d) ₹180
37. 37.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 6 days (d) 5 days
38. 38.If 4 mangoes cost ₹64, how much do 2 mangoes cost? (a) ₹48 (b) ₹128 (c) ₹32 (d) ₹62
39. 39.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 2 days (d) 10 days
40. 40.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 16 days (d) 11 days

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