Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 655 · 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. 1.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 8 days (d) 7 days
2. 2.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 5 days (c) 15 days (d) 9 days
3. 3.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹11 (b) ₹66 (c) ₹44 (d) ₹55
4. 4.If 2 mangoes cost ₹40, how much do 10 mangoes cost? (a) ₹48 (b) ₹220 (c) ₹400 (d) ₹200
5. 5.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 21 days (c) 48 days (d) 4 days
6. 6.₹119 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹17 (b) ₹85 (c) ₹34 (d) ₹102
7. 7.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 15 days
8. 8.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 6 days (d) 8 days
9. 9.If 4 pens cost ₹12, how much do 5 pens cost? (a) ₹18 (b) ₹13 (c) ₹60 (d) ₹15
10. 10.If 8 mangoes cost ₹176, how much do 4 mangoes cost? (a) ₹704 (b) ₹88 (c) ₹172 (d) ₹110
11. 11.If 2 kites cost ₹50, how much do 3 kites cost? (a) ₹75 (b) ₹51 (c) ₹100 (d) ₹150
12. 12.If 2 pens cost ₹28, how much do 11 pens cost? (a) ₹37 (b) ₹154 (c) ₹168 (d) ₹308
13. 13.₹133 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹19 (b) ₹57 (c) ₹95 (d) ₹76
14. 14.If 5 pens cost ₹35, how much do 12 pens cost? (a) ₹42 (b) ₹91 (c) ₹84 (d) ₹420
15. 15.If 6 pens cost ₹102, how much do 2 pens cost? (a) ₹204 (b) ₹98 (c) ₹51 (d) ₹34
16. 16.₹196 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹14 (b) ₹98 (c) ₹70 (d) ₹126
17. 17.₹260 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹160 (b) ₹130 (c) ₹20 (d) ₹100
18. 18.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 15 days (d) 3 days
19. 19.₹423 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹329 (b) ₹376 (c) ₹47 (d) ₹94
20. 20.If 5 pens cost ₹115, how much do 2 pens cost? (a) ₹112 (b) ₹230 (c) ₹69 (d) ₹46
21. 21.₹288 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹144 (b) ₹48 (c) ₹240 (d) ₹288
22. 22.₹253 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹23 (b) ₹184 (c) ₹69 (d) ₹207
23. 23.If 9 kites cost ₹72, how much do 10 kites cost? (a) ₹88 (b) ₹720 (c) ₹80 (d) ₹73
24. 24.If 5 notebooks cost ₹95, how much do 10 notebooks cost? (a) ₹100 (b) ₹190 (c) ₹950 (d) ₹209
25. 25.₹35 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹30 (b) ₹5 (c) ₹35 (d) ₹31
26. 26.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 11 days (d) 3 days
27. 27.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 26 days (b) 9 days (c) 27 days (d) 17 days
28. 28.If 4 pens cost ₹84, how much do 6 pens cost? (a) ₹147 (b) ₹86 (c) ₹126 (d) ₹504
29. 29.₹572 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹352 (b) ₹220 (c) ₹286 (d) ₹44
30. 30.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 3 days (d) 2 days
31. 31.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹105 (b) ₹75 (c) ₹15 (d) ₹90
32. 32.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 3 days (d) 1 day
33. 33.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹8 (b) ₹24 (c) ₹20 (d) ₹16
34. 34.₹350 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹200 (b) ₹50 (c) ₹150 (d) ₹175
35. 35.₹440 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹220 (b) ₹40 (c) ₹80 (d) ₹360
36. 36.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 2 days (d) 1 day
37. 37.₹387 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹215 (b) ₹172 (c) ₹43 (d) ₹258
38. 38.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 6 days (c) 8 days (d) 7 days
39. 39.₹20 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹20 (b) ₹5 (c) ₹10 (d) ₹15
40. 40.₹215 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹43 (b) ₹172 (c) ₹86 (d) ₹129

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