Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 295 · 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 9 pens cost ₹45, how much do 4 pens cost? (a) ₹40 (b) ₹180 (c) ₹20 (d) ₹25
2. 2.₹246 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹205 (b) ₹123 (c) ₹41 (d) ₹246
3. 3.If 9 kites cost ₹180, how much do 4 kites cost? (a) ₹720 (b) ₹100 (c) ₹175 (d) ₹80
4. 4.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹20 (b) ₹5 (c) ₹30 (d) ₹25
5. 5.If 3 kites cost ₹42, how much do 8 kites cost? (a) ₹126 (b) ₹112 (c) ₹47 (d) ₹336
6. 6.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 15 days (d) 22 days
7. 7.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 2 days (c) 8 days (d) 9 days
8. 8.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 4 days (c) 27 days (d) 3 days
9. 9.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 3 days (d) 6 days
10. 10.₹273 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹21 (b) ₹168 (c) ₹189 (d) ₹105
11. 11.If 9 notebooks cost ₹108, how much do 10 notebooks cost? (a) ₹1080 (b) ₹109 (c) ₹132 (d) ₹120
12. 12.₹230 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹230 (b) ₹115 (c) ₹207 (d) ₹23
13. 13.If 4 mangoes cost ₹12, how much do 3 mangoes cost? (a) ₹12 (b) ₹36 (c) ₹9 (d) ₹11
14. 14.₹81 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹73 (b) ₹9 (c) ₹72 (d) ₹81
15. 15.₹50 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹25 (b) ₹20 (c) ₹30 (d) ₹10
16. 16.₹385 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹280 (b) ₹315 (c) ₹105 (d) ₹35
17. 17.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 3 days (c) 29 days (d) 13 days
18. 18.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 20 days (b) 6 days (c) 5 days (d) 15 days
19. 19.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 4 days (d) 5 days
20. 20.₹264 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹132 (b) ₹110 (c) ₹22 (d) ₹154
21. 21.If 3 pens cost ₹30, how much do 6 pens cost? (a) ₹180 (b) ₹33 (c) ₹70 (d) ₹60
22. 22.₹550 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹400 (b) ₹150 (c) ₹50 (d) ₹275
23. 23.If 6 pens cost ₹78, how much do 4 pens cost? (a) ₹312 (b) ₹76 (c) ₹52 (d) ₹65
24. 24.₹88 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹8 (b) ₹44 (c) ₹64 (d) ₹24
25. 25.₹54 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹27 (b) ₹36 (c) ₹54 (d) ₹18
26. 26.5 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) 17 days (d) 25 days
27. 27.If 7 pens cost ₹56, how much do 6 pens cost? (a) ₹336 (b) ₹55 (c) ₹56 (d) ₹48
28. 28.₹162 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹81 (b) ₹18 (c) ₹72 (d) ₹90
29. 29.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 28 days (c) 7 days (d) 16 days
30. 30.6 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 14 days (d) 5 days
31. 31.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 13 days (d) 6 days
32. 32.₹392 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹196 (b) ₹343 (c) ₹49 (d) ₹392
33. 33.4 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) 15 days (d) 26 days
34. 34.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 1 day (d) 6 days
35. 35.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 26 days (d) 27 days
36. 36.If 8 mangoes cost ₹56, how much do 5 mangoes cost? (a) ₹42 (b) ₹53 (c) ₹35 (d) ₹280
37. 37.₹112 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹56 (b) ₹40 (c) ₹8 (d) ₹72
38. 38.If 6 pens cost ₹96, how much do 3 pens cost? (a) ₹288 (b) ₹93 (c) ₹48 (d) ₹64
39. 39.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 17 days (d) 11 days
40. 40.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 18 days (c) 2 days (d) 3 days

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