Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 568 · 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. 1.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 24 days (c) 6 days (d) 10 days
2. 2.₹84 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹48 (b) ₹36 (c) ₹42 (d) ₹12
3. 3.₹63 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹7 (b) ₹42 (c) ₹28 (d) ₹35
4. 4.If 9 mangoes cost ₹81, how much do 7 mangoes cost? (a) ₹79 (b) ₹567 (c) ₹72 (d) ₹63
5. 5.If 6 notebooks cost ₹24, how much do 3 notebooks cost? (a) ₹16 (b) ₹72 (c) ₹21 (d) ₹12
6. 6.If 3 kites cost ₹12, how much do 11 kites cost? (a) ₹20 (b) ₹44 (c) ₹132 (d) ₹48
7. 7.₹385 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹315 (b) ₹350 (c) ₹70 (d) ₹35
8. 8.₹126 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹63 (b) ₹45 (c) ₹81 (d) ₹9
9. 9.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 5 days (d) 4 days
10. 10.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 16 days (d) 7 days
11. 11.If 8 notebooks cost ₹40, how much do 9 notebooks cost? (a) ₹50 (b) ₹360 (c) ₹41 (d) ₹45
12. 12.₹121 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹110 (b) ₹99 (c) ₹11 (d) ₹22
13. 13.₹259 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹74 (b) ₹222 (c) ₹185 (d) ₹37
14. 14.If 6 kites cost ₹48, how much do 10 kites cost? (a) ₹88 (b) ₹480 (c) ₹80 (d) ₹52
15. 15.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 13 days (d) 4 days
16. 16.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 16 days (d) 5 days
17. 17.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 6 days (c) 31 days (d) 30 days
18. 18.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹17 (b) ₹119 (c) ₹85 (d) ₹102
19. 19.₹492 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹41 (b) ₹246 (c) ₹287 (d) ₹205
20. 20.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 11 days (d) 4 days
21. 21.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 2 days (d) 8 days
22. 22.If 8 kites cost ₹176, how much do 4 kites cost? (a) ₹110 (b) ₹88 (c) ₹704 (d) ₹172
23. 23.₹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
24. 24.If 8 mangoes cost ₹152, how much do 3 mangoes cost? (a) ₹57 (b) ₹147 (c) ₹76 (d) ₹456
25. 25.If 8 notebooks cost ₹184, how much do 12 notebooks cost? (a) ₹188 (b) ₹276 (c) ₹299 (d) ₹2208
26. 26.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 22 days (d) 21 days
27. 27.If 9 notebooks cost ₹72, how much do 2 notebooks cost? (a) ₹16 (b) ₹144 (c) ₹24 (d) ₹65
28. 28.If 6 notebooks cost ₹108, how much do 4 notebooks cost? (a) ₹90 (b) ₹72 (c) ₹106 (d) ₹432
29. 29.₹390 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹195 (b) ₹390 (c) ₹39 (d) ₹351
30. 30.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 16 days (d) 11 days
31. 31.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 19 days (d) 4 days
32. 32.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 11 days (d) 9 days
33. 33.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 17 days (c) 7 days (d) 32 days
34. 34.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 3 days (d) 6 days
35. 35.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 40 days (c) 9 days (d) 39 days
36. 36.₹124 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹124 (b) ₹93 (c) ₹31 (d) ₹62
37. 37.₹84 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹54 (b) ₹42 (c) ₹6 (d) ₹30
38. 38.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 2 days (d) 9 days
39. 39.7 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 14 days (b) 13 days (c) 15 days (d) 11 days
40. 40.If 3 mangoes cost ₹51, how much do 4 mangoes cost? (a) ₹85 (b) ₹204 (c) ₹52 (d) ₹68

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