Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 771 · 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 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 8 days (c) 15 days (d) 9 days
2. 2.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 40 days (c) 16 days (d) 41 days
3. 3.If 9 pens cost ₹117, how much do 7 pens cost? (a) ₹819 (b) ₹115 (c) ₹91 (d) ₹104
4. 4.If 8 kites cost ₹104, how much do 3 kites cost? (a) ₹312 (b) ₹39 (c) ₹52 (d) ₹99
5. 5.₹143 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹55 (b) ₹11 (c) ₹99 (d) ₹88
6. 6.If 5 mangoes cost ₹15, how much do 11 mangoes cost? (a) ₹21 (b) ₹165 (c) ₹33 (d) ₹36
7. 7.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 14 days (b) 2 days (c) 3 days (d) 18 days
8. 8.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹275 (b) ₹50 (c) ₹250 (d) ₹300
9. 9.If 3 mangoes cost ₹24, how much do 11 mangoes cost? (a) ₹264 (b) ₹88 (c) ₹32 (d) ₹96
10. 10.₹312 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹273 (b) ₹312 (c) ₹156 (d) ₹39
11. 11.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 1 day (c) 8 days (d) 7 days
12. 12.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 29 days (c) 8 days (d) 28 days
13. 13.If 6 kites cost ₹144, how much do 7 kites cost? (a) ₹145 (b) ₹192 (c) ₹168 (d) ₹1008
14. 14.If 2 pens cost ₹10, how much do 8 pens cost? (a) ₹40 (b) ₹45 (c) ₹80 (d) ₹16
15. 15.₹187 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹170 (b) ₹153 (c) ₹17 (d) ₹34
16. 16.₹154 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹22 (b) ₹110 (c) ₹77 (d) ₹44
17. 17.₹273 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹189 (b) ₹21 (c) ₹168 (d) ₹105
18. 18.₹45 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹31 (b) ₹15 (c) ₹45 (d) ₹30
19. 19.₹480 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹240 (d) ₹280
20. 20.If 4 notebooks cost ₹48, how much do 3 notebooks cost? (a) ₹48 (b) ₹144 (c) ₹47 (d) ₹36
21. 21.₹336 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹28 (b) ₹168 (c) ₹196 (d) ₹140
22. 22.4 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
23. 23.If 2 kites cost ₹50, how much do 10 kites cost? (a) ₹500 (b) ₹275 (c) ₹58 (d) ₹250
24. 24.₹55 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹30 (b) ₹25 (c) ₹35 (d) ₹5
25. 25.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 2 days (c) 9 days (d) 8 days
26. 26.If 2 pens cost ₹18, how much do 3 pens cost? (a) ₹19 (b) ₹54 (c) ₹27 (d) ₹36
27. 27.If 8 kites cost ₹24, how much do 2 kites cost? (a) ₹18 (b) ₹6 (c) ₹48 (d) ₹9
28. 28.If 3 notebooks cost ₹21, how much do 4 notebooks cost? (a) ₹28 (b) ₹22 (c) ₹35 (d) ₹84
29. 29.₹700 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹450 (b) ₹50 (c) ₹250 (d) ₹350
30. 30.₹350 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹35 (b) ₹175 (c) ₹315 (d) ₹350
31. 31.₹132 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹66 (b) ₹108 (c) ₹24 (d) ₹12
32. 32.₹175 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹70 (b) ₹35 (c) ₹105 (d) ₹140
33. 33.If 7 mangoes cost ₹133, how much do 4 mangoes cost? (a) ₹130 (b) ₹532 (c) ₹76 (d) ₹95
34. 34.If 3 kites cost ₹63, how much do 10 kites cost? (a) ₹630 (b) ₹210 (c) ₹70 (d) ₹231
35. 35.₹308 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹44 (b) ₹308 (c) ₹264 (d) ₹154
36. 36.₹162 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹135 (b) ₹81 (c) ₹27 (d) ₹162
37. 37.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 3 days (d) 15 days
38. 38.₹448 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹32 (b) ₹224 (c) ₹288 (d) ₹160
39. 39.If 5 pens cost ₹35, how much do 12 pens cost? (a) ₹84 (b) ₹42 (c) ₹420 (d) ₹91
40. 40.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 24 days (c) 14 days (d) 6 days

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