Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 306 · 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. 1.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 9 days (d) 8 days
2. 2.₹105 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹15 (b) ₹60 (c) ₹45 (d) ₹75
3. 3.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹117 (b) ₹18 (c) ₹162 (d) ₹72
4. 4.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 10 days
5. 5.If 7 kites cost ₹133, how much do 12 kites cost? (a) ₹138 (b) ₹228 (c) ₹247 (d) ₹1596
6. 6.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 28 days (d) 18 days
7. 7.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 2 days (d) 8 days
8. 8.₹198 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹99 (b) ₹18 (c) ₹108 (d) ₹90
9. 9.If 3 pens cost ₹66, how much do 4 pens cost? (a) ₹67 (b) ₹264 (c) ₹88 (d) ₹110
10. 10.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 6 days (c) 7 days (d) 5 days
11. 11.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 15 days (d) 6 days
12. 12.₹99 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹9 (b) ₹63 (c) ₹36 (d) ₹72
13. 13.₹42 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹21 (b) ₹7 (c) ₹42 (d) ₹35
14. 14.₹406 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹29 (b) ₹145 (c) ₹203 (d) ₹261
15. 15.If 2 pens cost ₹48, how much do 9 pens cost? (a) ₹432 (b) ₹55 (c) ₹240 (d) ₹216
16. 16.₹588 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹378 (b) ₹210 (c) ₹294 (d) ₹42
17. 17.₹306 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹238 (b) ₹34 (c) ₹153 (d) ₹68
18. 18.If 2 notebooks cost ₹40, how much do 12 notebooks cost? (a) ₹50 (b) ₹260 (c) ₹240 (d) ₹480
19. 19.₹48 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹40 (b) ₹24 (c) ₹8 (d) ₹48
20. 20.₹35 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹20 (b) ₹15 (c) ₹5 (d) ₹25
21. 21.If 7 notebooks cost ₹21, how much do 3 notebooks cost? (a) ₹17 (b) ₹12 (c) ₹9 (d) ₹63
22. 22.₹329 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹235 (b) ₹282 (c) ₹47 (d) ₹94
23. 23.If 3 mangoes cost ₹9, how much do 7 mangoes cost? (a) ₹21 (b) ₹13 (c) ₹24 (d) ₹63
24. 24.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 7 days
25. 25.₹81 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹54 (b) ₹45 (c) ₹9 (d) ₹36
26. 26.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 7 days (d) 8 days
27. 27.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 15 days (c) 16 days (d) 13 days
28. 28.₹369 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹328 (b) ₹329 (c) ₹41 (d) ₹369
29. 29.If 2 pens cost ₹8, how much do 8 pens cost? (a) ₹64 (b) ₹36 (c) ₹14 (d) ₹32
30. 30.If 7 kites cost ₹91, how much do 9 kites cost? (a) ₹117 (b) ₹93 (c) ₹130 (d) ₹819
31. 31.If 6 mangoes cost ₹54, how much do 3 mangoes cost? (a) ₹27 (b) ₹36 (c) ₹162 (d) ₹51
32. 32.₹280 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹196 (b) ₹84 (c) ₹140 (d) ₹28
33. 33.If 5 kites cost ₹35, how much do 2 kites cost? (a) ₹70 (b) ₹14 (c) ₹32 (d) ₹21
34. 34.₹195 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹120 (b) ₹135 (c) ₹15 (d) ₹75
35. 35.₹170 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹17 (b) ₹153 (c) ₹85 (d) ₹170
36. 36.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 13 days (c) 28 days (d) 1 day
37. 37.If 5 mangoes cost ₹105, how much do 10 mangoes cost? (a) ₹1050 (b) ₹210 (c) ₹231 (d) ₹110
38. 38.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 40 days (c) 39 days (d) 17 days
39. 39.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 9 days (d) 21 days
40. 40.₹572 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹220 (b) ₹44 (c) ₹352 (d) ₹286

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