Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 89 · 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 3 kites cost ₹69, how much do 12 kites cost? (a) ₹276 (b) ₹828 (c) ₹78 (d) ₹299
2. 2.₹220 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹110 (b) ₹160 (c) ₹60 (d) ₹20
3. 3.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 7 days (d) 2 days
4. 4.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 17 days (d) 25 days
5. 5.If 4 kites cost ₹60, how much do 11 kites cost? (a) ₹660 (b) ₹180 (c) ₹165 (d) ₹67
6. 6.₹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
7. 7.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 3 days (d) 8 days
8. 8.If 5 mangoes cost ₹25, how much do 9 mangoes cost? (a) ₹45 (b) ₹225 (c) ₹29 (d) ₹50
9. 9.₹232 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹116 (b) ₹145 (c) ₹87 (d) ₹29
10. 10.If 5 mangoes cost ₹70, how much do 6 mangoes cost? (a) ₹71 (b) ₹98 (c) ₹84 (d) ₹420
11. 11.₹161 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹69 (b) ₹92 (c) ₹115 (d) ₹23
12. 12.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 3 days (d) 10 days
13. 13.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 35 days (c) 36 days (d) 19 days
14. 14.8 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) 9 days (d) 8 days
15. 15.If 6 mangoes cost ₹60, how much do 12 mangoes cost? (a) ₹120 (b) ₹130 (c) ₹720 (d) ₹66
16. 16.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 9 days (d) 1 day
17. 17.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 7 days (d) 10 days
18. 18.₹250 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹125 (b) ₹50 (c) ₹150 (d) ₹100
19. 19.₹196 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹84 (b) ₹98 (c) ₹112 (d) ₹28
20. 20.If 9 kites cost ₹216, how much do 5 kites cost? (a) ₹1080 (b) ₹144 (c) ₹212 (d) ₹120
21. 21.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 9 days (d) 7 days
22. 22.₹80 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹48 (b) ₹16 (c) ₹40 (d) ₹32
23. 23.₹49 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹21 (b) ₹7 (c) ₹35 (d) ₹28
24. 24.If 7 pens cost ₹56, how much do 12 pens cost? (a) ₹104 (b) ₹672 (c) ₹96 (d) ₹61
25. 25.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 7 days
26. 26.₹473 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹301 (b) ₹344 (c) ₹43 (d) ₹172
27. 27.If 6 pens cost ₹84, how much do 9 pens cost? (a) ₹126 (b) ₹87 (c) ₹756 (d) ₹140
28. 28.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 5 days (c) 9 days (d) 8 days
29. 29.If 8 notebooks cost ₹56, how much do 9 notebooks cost? (a) ₹504 (b) ₹70 (c) ₹63 (d) ₹57
30. 30.If 4 pens cost ₹84, how much do 3 pens cost? (a) ₹83 (b) ₹84 (c) ₹63 (d) ₹252
31. 31.₹175 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹35 (b) ₹141 (c) ₹140 (d) ₹175
32. 32.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 23 days (d) 22 days
33. 33.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 6 days (c) 4 days (d) 10 days
34. 34.If 9 pens cost ₹81, how much do 3 pens cost? (a) ₹36 (b) ₹27 (c) ₹75 (d) ₹243
35. 35.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 29 days (c) 3 days (d) 13 days
36. 36.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 20 days (c) 5 days (d) 6 days
37. 37.₹364 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹28 (b) ₹140 (c) ₹224 (d) ₹182
38. 38.₹84 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹42 (b) ₹12 (c) ₹60 (d) ₹24
39. 39.If 8 notebooks cost ₹48, how much do 6 notebooks cost? (a) ₹42 (b) ₹46 (c) ₹288 (d) ₹36
40. 40.₹328 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹164 (b) ₹41 (c) ₹287 (d) ₹328

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