Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 912 · 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. 1.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 3 days (d) 4 days
2. 2.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹18 (b) ₹162 (c) ₹72 (d) ₹117
3. 3.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 22 days (d) 15 days
4. 4.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 7 days (d) 6 days
5. 5.If 6 pens cost ₹90, how much do 7 pens cost? (a) ₹105 (b) ₹630 (c) ₹91 (d) ₹120
6. 6.₹162 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹162 (b) ₹27 (c) ₹135 (d) ₹81
7. 7.If 3 kites cost ₹72, how much do 10 kites cost? (a) ₹720 (b) ₹79 (c) ₹264 (d) ₹240
8. 8.If 3 mangoes cost ₹9, how much do 10 mangoes cost? (a) ₹16 (b) ₹90 (c) ₹33 (d) ₹30
9. 9.If 2 notebooks cost ₹8, how much do 10 notebooks cost? (a) ₹44 (b) ₹16 (c) ₹80 (d) ₹40
10. 10.If 7 kites cost ₹21, how much do 9 kites cost? (a) ₹30 (b) ₹189 (c) ₹27 (d) ₹23
11. 11.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 15 days (d) 14 days
12. 12.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 11 days (b) 6 days (c) 7 days (d) 8 days
13. 13.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 14 days (d) 5 days
14. 14.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 4 days (d) 10 days
15. 15.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹14 (b) ₹7 (c) ₹21 (d) ₹28
16. 16.If 8 pens cost ₹168, how much do 3 pens cost? (a) ₹63 (b) ₹504 (c) ₹84 (d) ₹163
17. 17.₹396 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹33 (b) ₹165 (c) ₹198 (d) ₹231
18. 18.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 7 days (d) 2 days
19. 19.If 7 mangoes cost ₹49, how much do 8 mangoes cost? (a) ₹50 (b) ₹392 (c) ₹56 (d) ₹63
20. 20.6 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 19 days (c) 25 days (d) 11 days
21. 21.₹121 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹11 (b) ₹77 (c) ₹66 (d) ₹55
22. 22.₹259 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹222 (b) ₹185 (c) ₹37 (d) ₹74
23. 23.If 2 kites cost ₹12, how much do 9 kites cost? (a) ₹108 (b) ₹60 (c) ₹19 (d) ₹54
24. 24.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 2 days (c) 3 days (d) 4 days
25. 25.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹126 (b) ₹147 (c) ₹105 (d) ₹21
26. 26.If 7 kites cost ₹112, how much do 2 kites cost? (a) ₹224 (b) ₹32 (c) ₹107 (d) ₹48
27. 27.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 12 days (d) 6 days
28. 28.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 9 days (d) 3 days
29. 29.If 5 mangoes cost ₹55, how much do 12 mangoes cost? (a) ₹660 (b) ₹62 (c) ₹132 (d) ₹143
30. 30.₹528 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹96 (b) ₹432 (c) ₹48 (d) ₹264
31. 31.₹210 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹30 (b) ₹210 (c) ₹105 (d) ₹180
32. 32.If 3 mangoes cost ₹75, how much do 11 mangoes cost? (a) ₹300 (b) ₹275 (c) ₹825 (d) ₹83
33. 33.₹420 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹210 (b) ₹150 (c) ₹30 (d) ₹270
34. 34.₹100 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹30 (b) ₹50 (c) ₹10 (d) ₹70
35. 35.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 2 days (d) 8 days
36. 36.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 5 days (d) 10 days
37. 37.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 10 days (c) 8 days (d) 13 days
38. 38.₹110 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹55 (b) ₹70 (c) ₹10 (d) ₹40
39. 39.₹152 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹19 (b) ₹133 (c) ₹152 (d) ₹76
40. 40.If 8 kites cost ₹184, how much do 9 kites cost? (a) ₹1656 (b) ₹207 (c) ₹230 (d) ₹185

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