Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 605 · 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.₹585 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹405 (b) ₹45 (c) ₹360 (d) ₹225
2. 2.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 10 days (d) 18 days
3. 3.₹210 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹210 (b) ₹42 (c) ₹168 (d) ₹105
4. 4.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 15 days
5. 5.If 3 notebooks cost ₹12, how much do 4 notebooks cost? (a) ₹48 (b) ₹20 (c) ₹16 (d) ₹13
6. 6.If 9 pens cost ₹135, how much do 4 pens cost? (a) ₹130 (b) ₹75 (c) ₹60 (d) ₹540
7. 7.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 3 days (c) 27 days (d) 5 days
8. 8.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 1 day (d) 17 days
9. 9.If 2 mangoes cost ₹10, how much do 8 mangoes cost? (a) ₹40 (b) ₹16 (c) ₹80 (d) ₹45
10. 10.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 49 days (c) 19 days (d) 4 days
11. 11.8 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 20 days (c) 41 days (d) 40 days
12. 12.If 6 mangoes cost ₹96, how much do 7 mangoes cost? (a) ₹112 (b) ₹128 (c) ₹97 (d) ₹672
13. 13.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 6 days (c) 7 days (d) 5 days
14. 14.If 2 mangoes cost ₹50, how much do 4 mangoes cost? (a) ₹52 (b) ₹125 (c) ₹200 (d) ₹100
15. 15.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 45 days (c) 19 days (d) 5 days
16. 16.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 11 days (d) 1 day
17. 17.If 7 pens cost ₹70, how much do 9 pens cost? (a) ₹72 (b) ₹90 (c) ₹630 (d) ₹100
18. 18.If 4 mangoes cost ₹20, how much do 6 mangoes cost? (a) ₹30 (b) ₹35 (c) ₹120 (d) ₹22
19. 19.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 13 days (d) 5 days
20. 20.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 5 days (d) 4 days
21. 21.If 9 mangoes cost ₹198, how much do 5 mangoes cost? (a) ₹132 (b) ₹194 (c) ₹110 (d) ₹990
22. 22.₹287 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹246 (b) ₹82 (c) ₹41 (d) ₹205
23. 23.If 4 kites cost ₹80, how much do 12 kites cost? (a) ₹240 (b) ₹960 (c) ₹260 (d) ₹88
24. 24.₹286 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹104 (b) ₹26 (c) ₹182 (d) ₹143
25. 25.₹473 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹387 (b) ₹129 (c) ₹43 (d) ₹344
26. 26.₹336 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹336 (b) ₹168 (c) ₹294 (d) ₹42
27. 27.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 12 days (d) 16 days
28. 28.₹65 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹39 (b) ₹26 (c) ₹13 (d) ₹52
29. 29.If 4 kites cost ₹20, how much do 12 kites cost? (a) ₹240 (b) ₹28 (c) ₹60 (d) ₹65
30. 30.3 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
31. 31.If 4 mangoes cost ₹76, how much do 2 mangoes cost? (a) ₹57 (b) ₹74 (c) ₹38 (d) ₹152
32. 32.If 4 pens cost ₹32, how much do 2 pens cost? (a) ₹16 (b) ₹64 (c) ₹30 (d) ₹24
33. 33.₹45 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹18 (b) ₹27 (c) ₹9 (d) ₹36
34. 34.If 3 pens cost ₹66, how much do 8 pens cost? (a) ₹528 (b) ₹71 (c) ₹198 (d) ₹176
35. 35.If 5 kites cost ₹60, how much do 11 kites cost? (a) ₹144 (b) ₹132 (c) ₹660 (d) ₹66
36. 36.₹165 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹15 (b) ₹135 (c) ₹150 (d) ₹30
37. 37.₹288 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹144 (b) ₹160 (c) ₹128 (d) ₹32
38. 38.₹468 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹288 (b) ₹36 (c) ₹180 (d) ₹234
39. 39.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 2 days (c) 12 days (d) 19 days
40. 40.If 5 mangoes cost ₹20, how much do 10 mangoes cost? (a) ₹25 (b) ₹200 (c) ₹40 (d) ₹44

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