Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 534 · 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. 1.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 13 days (d) 10 days
2. 2.If 2 pens cost ₹32, how much do 6 pens cost? (a) ₹112 (b) ₹96 (c) ₹36 (d) ₹192
3. 3.₹99 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹63 (b) ₹36 (c) ₹9 (d) ₹72
4. 4.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 34 days (c) 5 days (d) 33 days
5. 5.₹88 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹22 (b) ₹88 (c) ₹66 (d) ₹44
6. 6.If 4 pens cost ₹20, how much do 2 pens cost? (a) ₹10 (b) ₹18 (c) ₹15 (d) ₹40
7. 7.If 9 pens cost ₹45, how much do 4 pens cost? (a) ₹40 (b) ₹180 (c) ₹20 (d) ₹25
8. 8.If 8 notebooks cost ₹80, how much do 9 notebooks cost? (a) ₹100 (b) ₹720 (c) ₹81 (d) ₹90
9. 9.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 40 days (c) 39 days (d) 9 days
10. 10.₹324 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹135 (b) ₹162 (c) ₹27 (d) ₹189
11. 11.8 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
12. 12.If 9 kites cost ₹198, how much do 5 kites cost? (a) ₹990 (b) ₹194 (c) ₹110 (d) ₹132
13. 13.If 4 mangoes cost ₹64, how much do 6 mangoes cost? (a) ₹96 (b) ₹66 (c) ₹112 (d) ₹384
14. 14.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 27 days (c) 3 days (d) 5 days
15. 15.If 3 pens cost ₹9, how much do 8 pens cost? (a) ₹14 (b) ₹27 (c) ₹24 (d) ₹72
16. 16.If 2 mangoes cost ₹48, how much do 7 mangoes cost? (a) ₹336 (b) ₹168 (c) ₹192 (d) ₹53
17. 17.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 16 days (d) 11 days
18. 18.₹220 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹110 (b) ₹20 (c) ₹100 (d) ₹120
19. 19.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 5 days (d) 4 days
20. 20.If 6 kites cost ₹126, how much do 3 kites cost? (a) ₹378 (b) ₹63 (c) ₹84 (d) ₹123
21. 21.₹385 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹35 (b) ₹210 (c) ₹245 (d) ₹175
22. 22.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 7 days (d) 1 day
23. 23.If 7 kites cost ₹28, how much do 4 kites cost? (a) ₹20 (b) ₹25 (c) ₹16 (d) ₹112
24. 24.₹221 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹85 (b) ₹136 (c) ₹153 (d) ₹17
25. 25.If 8 pens cost ₹152, how much do 7 pens cost? (a) ₹152 (b) ₹133 (c) ₹151 (d) ₹1064
26. 26.₹429 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹297 (b) ₹165 (c) ₹264 (d) ₹33
27. 27.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹21 (b) ₹28 (c) ₹14 (d) ₹7
28. 28.₹506 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹46 (b) ₹322 (c) ₹253 (d) ₹184
29. 29.₹240 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹24 (b) ₹216 (c) ₹240 (d) ₹120
30. 30.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 15 days (d) 5 days
31. 31.If 9 mangoes cost ₹225, how much do 4 mangoes cost? (a) ₹900 (b) ₹220 (c) ₹100 (d) ₹125
32. 32.₹104 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹39 (b) ₹13 (c) ₹52 (d) ₹65
33. 33.₹287 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹41 (b) ₹164 (c) ₹123 (d) ₹205
34. 34.₹44 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹11 (b) ₹22 (c) ₹44 (d) ₹33
35. 35.If 9 kites cost ₹36, how much do 10 kites cost? (a) ₹360 (b) ₹44 (c) ₹37 (d) ₹40
36. 36.₹624 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹312 (b) ₹48 (c) ₹192 (d) ₹432
37. 37.If 9 notebooks cost ₹135, how much do 12 notebooks cost? (a) ₹138 (b) ₹180 (c) ₹195 (d) ₹1620
38. 38.₹312 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹156 (b) ₹39 (c) ₹312 (d) ₹273
39. 39.₹42 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹6 (b) ₹21 (c) ₹42 (d) ₹36
40. 40.₹546 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹273 (b) ₹351 (c) ₹195 (d) ₹39

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