Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 730 · 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.₹69 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹69 (b) ₹47 (c) ₹23 (d) ₹46
2. 2.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 33 days (c) 14 days (d) 32 days
3. 3.If 7 notebooks cost ₹140, how much do 3 notebooks cost? (a) ₹60 (b) ₹80 (c) ₹420 (d) ₹136
4. 4.If 3 pens cost ₹33, how much do 4 pens cost? (a) ₹34 (b) ₹55 (c) ₹132 (d) ₹44
5. 5.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 1 day (d) 16 days
6. 6.If 8 pens cost ₹144, how much do 3 pens cost? (a) ₹139 (b) ₹432 (c) ₹54 (d) ₹72
7. 7.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 5 days (d) 14 days
8. 8.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 9 days (d) 16 days
9. 9.If 6 pens cost ₹84, how much do 8 pens cost? (a) ₹112 (b) ₹672 (c) ₹86 (d) ₹126
10. 10.4 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) 16 days (d) 7 days
11. 11.₹377 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹29 (b) ₹116 (c) ₹261 (d) ₹290
12. 12.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 8 days (d) 9 days
13. 13.₹180 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹180 (b) ₹162 (c) ₹90 (d) ₹18
14. 14.₹261 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹116 (b) ₹29 (c) ₹174 (d) ₹145
15. 15.₹462 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹168 (b) ₹42 (c) ₹294 (d) ₹231
16. 16.If 8 notebooks cost ₹40, how much do 12 notebooks cost? (a) ₹44 (b) ₹65 (c) ₹480 (d) ₹60
17. 17.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 13 days (c) 22 days (d) 9 days
18. 18.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 4 days (d) 5 days
19. 19.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 10 days (d) 4 days
20. 20.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 12 days (d) 11 days
21. 21.₹420 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹294 (b) ₹126 (c) ₹210 (d) ₹42
22. 22.₹117 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹104 (b) ₹91 (c) ₹26 (d) ₹13
23. 23.₹294 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹147 (b) ₹168 (c) ₹42 (d) ₹126
24. 24.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 20 days (c) 21 days (d) 10 days
25. 25.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 12 days (d) 4 days
26. 26.₹88 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹56 (b) ₹32 (c) ₹44 (d) ₹8
27. 27.₹532 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹190 (b) ₹266 (c) ₹38 (d) ₹342
28. 28.If 4 pens cost ₹68, how much do 8 pens cost? (a) ₹136 (b) ₹153 (c) ₹544 (d) ₹72
29. 29.₹288 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹144 (b) ₹168 (c) ₹120 (d) ₹24
30. 30.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 53 days (d) 52 days
31. 31.₹506 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹46 (b) ₹138 (c) ₹368 (d) ₹253
32. 32.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 49 days (d) 9 days
33. 33.If 7 pens cost ₹154, how much do 8 pens cost? (a) ₹1232 (b) ₹198 (c) ₹176 (d) ₹155
34. 34.If 5 mangoes cost ₹20, how much do 6 mangoes cost? (a) ₹21 (b) ₹120 (c) ₹28 (d) ₹24
35. 35.If 9 mangoes cost ₹207, how much do 2 mangoes cost? (a) ₹46 (b) ₹414 (c) ₹200 (d) ₹69
36. 36.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 7 days (d) 9 days
37. 37.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 7 days (d) 1 day
38. 38.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹35 (b) ₹42 (c) ₹49 (d) ₹7
39. 39.If 7 notebooks cost ₹84, how much do 2 notebooks cost? (a) ₹168 (b) ₹79 (c) ₹36 (d) ₹24
40. 40.₹405 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹90 (b) ₹315 (c) ₹45 (d) ₹360

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