Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 999 · 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. 1.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 6 days (d) 7 days
2. 2.₹480 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹480 (b) ₹48 (c) ₹432 (d) ₹240
3. 3.If 9 notebooks cost ₹153, how much do 12 notebooks cost? (a) ₹156 (b) ₹204 (c) ₹221 (d) ₹1836
4. 4.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 3 days (d) 8 days
5. 5.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 2 days (b) 12 days (c) 3 days (d) 18 days
6. 6.If 3 kites cost ₹15, how much do 7 kites cost? (a) ₹40 (b) ₹19 (c) ₹35 (d) ₹105
7. 7.3 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
8. 8.₹242 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹22 (b) ₹121 (c) ₹66 (d) ₹176
9. 9.If 9 mangoes cost ₹27, how much do 10 mangoes cost? (a) ₹28 (b) ₹30 (c) ₹270 (d) ₹33
10. 10.If 9 kites cost ₹162, how much do 6 kites cost? (a) ₹972 (b) ₹108 (c) ₹159 (d) ₹126
11. 11.₹99 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹89 (b) ₹99 (c) ₹11 (d) ₹88
12. 12.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 25 days (d) 17 days
13. 13.If 9 mangoes cost ₹225, how much do 7 mangoes cost? (a) ₹223 (b) ₹175 (c) ₹1575 (d) ₹200
14. 14.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 11 days (d) 13 days
15. 15.If 4 mangoes cost ₹48, how much do 11 mangoes cost? (a) ₹55 (b) ₹132 (c) ₹144 (d) ₹528
16. 16.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 17 days
17. 17.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 7 days (d) 12 days
18. 18.₹168 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹28 (b) ₹140 (c) ₹168 (d) ₹84
19. 19.If 7 kites cost ₹119, how much do 8 kites cost? (a) ₹120 (b) ₹952 (c) ₹153 (d) ₹136
20. 20.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 2 days (d) 3 days
21. 21.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 40 days (c) 39 days (d) 19 days
22. 22.₹77 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹28 (b) ₹7 (c) ₹49 (d) ₹56
23. 23.If 6 pens cost ₹48, how much do 2 pens cost? (a) ₹16 (b) ₹96 (c) ₹24 (d) ₹44
24. 24.If 8 pens cost ₹32, how much do 5 pens cost? (a) ₹29 (b) ₹24 (c) ₹160 (d) ₹20
25. 25.₹28 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹7 (b) ₹14 (c) ₹28 (d) ₹21
26. 26.If 4 notebooks cost ₹28, how much do 7 notebooks cost? (a) ₹56 (b) ₹49 (c) ₹196 (d) ₹31
27. 27.If 3 pens cost ₹60, how much do 12 pens cost? (a) ₹240 (b) ₹720 (c) ₹69 (d) ₹260
28. 28.If 2 pens cost ₹12, how much do 9 pens cost? (a) ₹108 (b) ₹19 (c) ₹60 (d) ₹54
29. 29.₹91 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹13 (b) ₹65 (c) ₹52 (d) ₹39
30. 30.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 27 days (c) 17 days (d) 26 days
31. 31.If 2 notebooks cost ₹8, how much do 9 notebooks cost? (a) ₹15 (b) ₹40 (c) ₹36 (d) ₹72
32. 32.If 5 notebooks cost ₹115, how much do 4 notebooks cost? (a) ₹460 (b) ₹115 (c) ₹114 (d) ₹92
33. 33.₹88 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹88 (b) ₹22 (c) ₹66 (d) ₹44
34. 34.₹279 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹248 (b) ₹279 (c) ₹31 (d) ₹249
35. 35.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 23 days (c) 9 days (d) 22 days
36. 36.₹564 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹235 (b) ₹329 (c) ₹282 (d) ₹47
37. 37.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 2 days (d) 8 days
38. 38.If 4 pens cost ₹44, how much do 2 pens cost? (a) ₹88 (b) ₹33 (c) ₹22 (d) ₹42
39. 39.If 8 pens cost ₹40, how much do 12 pens cost? (a) ₹65 (b) ₹44 (c) ₹480 (d) ₹60
40. 40.If 9 kites cost ₹117, how much do 2 kites cost? (a) ₹234 (b) ₹110 (c) ₹26 (d) ₹39

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