Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 506 · 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 11 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 7 days (c) 15 days (d) 34 days
2. 2.If 9 mangoes cost ₹45, how much do 6 mangoes cost? (a) ₹270 (b) ₹30 (c) ₹42 (d) ₹35
3. 3.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 17 days
4. 4.If 6 mangoes cost ₹60, how much do 12 mangoes cost? (a) ₹720 (b) ₹66 (c) ₹130 (d) ₹120
5. 5.If 4 notebooks cost ₹60, how much do 3 notebooks cost? (a) ₹59 (b) ₹60 (c) ₹180 (d) ₹45
6. 6.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 6 days (c) 5 days (d) 7 days
7. 7.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 15 days (d) 14 days
8. 8.6 workers can build a wall in 14 days. How many days will 12 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 8 days (d) 20 days
9. 9.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 11 days (c) 26 days (d) 15 days
10. 10.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹84 (b) ₹12 (c) ₹60 (d) ₹108
11. 11.₹468 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹234 (b) ₹144 (c) ₹36 (d) ₹324
12. 12.If 9 pens cost ₹36, how much do 11 pens cost? (a) ₹396 (b) ₹38 (c) ₹48 (d) ₹44
13. 13.If 4 mangoes cost ₹12, how much do 2 mangoes cost? (a) ₹10 (b) ₹9 (c) ₹6 (d) ₹24
14. 14.₹115 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹23 (b) ₹115 (c) ₹93 (d) ₹92
15. 15.₹273 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹78 (b) ₹234 (c) ₹39 (d) ₹195
16. 16.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 3 days (d) 4 days
17. 17.If 3 kites cost ₹72, how much do 11 kites cost? (a) ₹288 (b) ₹792 (c) ₹80 (d) ₹264
18. 18.₹132 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹22 (b) ₹110 (c) ₹66 (d) ₹132
19. 19.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 21 days (d) 22 days
20. 20.₹40 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹40 (b) ₹32 (c) ₹20 (d) ₹8
21. 21.If 2 kites cost ₹18, how much do 5 kites cost? (a) ₹90 (b) ₹21 (c) ₹45 (d) ₹54
22. 22.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 8 days (d) 4 days
23. 23.₹108 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹12 (b) ₹54 (c) ₹48 (d) ₹60
24. 24.If 2 pens cost ₹46, how much do 3 pens cost? (a) ₹92 (b) ₹69 (c) ₹138 (d) ₹47
25. 25.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 4 days (d) 13 days
26. 26.If 6 notebooks cost ₹150, how much do 5 notebooks cost? (a) ₹149 (b) ₹750 (c) ₹150 (d) ₹125
27. 27.If 2 notebooks cost ₹12, how much do 11 notebooks cost? (a) ₹132 (b) ₹66 (c) ₹72 (d) ₹21
28. 28.₹216 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹108 (b) ₹27 (c) ₹135 (d) ₹81
29. 29.₹144 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹60 (b) ₹84 (c) ₹72 (d) ₹12
30. 30.If 8 mangoes cost ₹112, how much do 2 mangoes cost? (a) ₹224 (b) ₹106 (c) ₹42 (d) ₹28
31. 31.₹48 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹6 (b) ₹24 (c) ₹42 (d) ₹48
32. 32.9 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 7 days (d) 8 days
33. 33.If 4 kites cost ₹40, how much do 5 kites cost? (a) ₹50 (b) ₹60 (c) ₹200 (d) ₹41
34. 34.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 17 days (d) 9 days
35. 35.₹55 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹22 (b) ₹11 (c) ₹44 (d) ₹33
36. 36.₹550 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹50 (b) ₹200 (c) ₹350 (d) ₹275
37. 37.If 5 pens cost ₹75, how much do 12 pens cost? (a) ₹82 (b) ₹900 (c) ₹180 (d) ₹195
38. 38.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 5 days (c) 7 days (d) 6 days
39. 39.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 5 days (d) 6 days
40. 40.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 19 days (b) 16 days (c) 18 days (d) 12 days

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