Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 980 · 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 ₹27, how much do 12 pens cost? (a) ₹30 (b) ₹36 (c) ₹39 (d) ₹324
2. 2.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 8 days (c) 6 days (d) 24 days
3. 3.If 4 notebooks cost ₹44, how much do 11 notebooks cost? (a) ₹484 (b) ₹121 (c) ₹51 (d) ₹132
4. 4.If 6 kites cost ₹36, how much do 2 kites cost? (a) ₹72 (b) ₹18 (c) ₹12 (d) ₹32
5. 5.₹224 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹196 (b) ₹28 (c) ₹112 (d) ₹224
6. 6.If 6 kites cost ₹150, how much do 12 kites cost? (a) ₹300 (b) ₹1800 (c) ₹325 (d) ₹156
7. 7.₹104 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹13 (b) ₹39 (c) ₹52 (d) ₹65
8. 8.₹60 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹12 (b) ₹30 (c) ₹36 (d) ₹24
9. 9.₹182 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹70 (b) ₹91 (c) ₹14 (d) ₹112
10. 10.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 3 days (d) 6 days
11. 11.7 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) 14 days (d) 15 days
12. 12.If 9 pens cost ₹225, how much do 8 pens cost? (a) ₹1800 (b) ₹225 (c) ₹200 (d) ₹224
13. 13.₹121 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹77 (b) ₹11 (c) ₹55 (d) ₹66
14. 14.If 2 pens cost ₹12, how much do 9 pens cost? (a) ₹19 (b) ₹108 (c) ₹60 (d) ₹54
15. 15.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹196 (b) ₹140 (c) ₹28 (d) ₹252
16. 16.₹245 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹140 (b) ₹35 (c) ₹175 (d) ₹105
17. 17.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 9 days (d) 49 days
18. 18.If 2 notebooks cost ₹42, how much do 3 notebooks cost? (a) ₹43 (b) ₹63 (c) ₹126 (d) ₹84
19. 19.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 6 days (d) 5 days
20. 20.9 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) 8 days (d) 9 days
21. 21.₹539 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹294 (b) ₹343 (c) ₹245 (d) ₹49
22. 22.₹57 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹38 (b) ₹39 (c) ₹19 (d) ₹57
23. 23.If 5 pens cost ₹110, how much do 12 pens cost? (a) ₹264 (b) ₹1320 (c) ₹117 (d) ₹286
24. 24.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 11 days (c) 5 days (d) 20 days
25. 25.₹96 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹80 (b) ₹96 (c) ₹48 (d) ₹16
26. 26.6 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
27. 27.₹611 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹423 (b) ₹47 (c) ₹235 (d) ₹376
28. 28.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 10 days (d) 7 days
29. 29.₹18 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹9 (b) ₹18 (c) ₹12 (d) ₹6
30. 30.₹129 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹129 (b) ₹87 (c) ₹86 (d) ₹43
31. 31.If 7 notebooks cost ₹133, how much do 11 notebooks cost? (a) ₹137 (b) ₹1463 (c) ₹209 (d) ₹228
32. 32.₹378 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹243 (b) ₹135 (c) ₹189 (d) ₹27
33. 33.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 12 days (d) 1 day
34. 34.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 7 days (d) 10 days
35. 35.₹115 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹69 (b) ₹92 (c) ₹46 (d) ₹23
36. 36.If 4 notebooks cost ₹24, how much do 11 notebooks cost? (a) ₹66 (b) ₹72 (c) ₹31 (d) ₹264
37. 37.₹484 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹44 (b) ₹242 (c) ₹396 (d) ₹88
38. 38.If 3 pens cost ₹12, how much do 9 pens cost? (a) ₹36 (b) ₹108 (c) ₹40 (d) ₹18
39. 39.₹119 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹103 (b) ₹102 (c) ₹119 (d) ₹17
40. 40.₹306 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹238 (b) ₹68 (c) ₹34 (d) ₹153

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