Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 966 · 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. 1.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 2 days (d) 3 days
2. 2.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 13 days (d) 15 days
3. 3.7 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) 8 days (d) 7 days
4. 4.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 45 days (c) 9 days (d) 5 days
5. 5.₹528 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹144 (b) ₹384 (c) ₹48 (d) ₹264
6. 6.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 9 days (d) 10 days
7. 7.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 14 days (d) 16 days
8. 8.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹14 (b) ₹70 (c) ₹84 (d) ₹98
9. 9.₹256 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹32 (b) ₹96 (c) ₹128 (d) ₹160
10. 10.₹80 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹40 (b) ₹24 (c) ₹56 (d) ₹8
11. 11.₹100 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹10 (b) ₹100 (c) ₹90 (d) ₹50
12. 12.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 15 days (d) 7 days
13. 13.₹45 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹5 (b) ₹45 (c) ₹41 (d) ₹40
14. 14.₹200 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹180 (b) ₹20 (c) ₹200 (d) ₹100
15. 15.If 4 pens cost ₹24, how much do 3 pens cost? (a) ₹24 (b) ₹23 (c) ₹18 (d) ₹72
16. 16.If 5 mangoes cost ₹90, how much do 10 mangoes cost? (a) ₹900 (b) ₹180 (c) ₹95 (d) ₹198
17. 17.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 13 days
18. 18.₹273 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹21 (b) ₹210 (c) ₹84 (d) ₹189
19. 19.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 13 days (c) 9 days (d) 15 days
20. 20.₹87 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹87 (b) ₹58 (c) ₹59 (d) ₹29
21. 21.₹45 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹45 (b) ₹36 (c) ₹37 (d) ₹9
22. 22.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 3 days (d) 11 days
23. 23.₹153 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹17 (b) ₹34 (c) ₹119 (d) ₹136
24. 24.₹154 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹132 (b) ₹77 (c) ₹154 (d) ₹22
25. 25.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 19 days (c) 2 days (d) 4 days
26. 26.₹152 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹152 (b) ₹76 (c) ₹19 (d) ₹133
27. 27.₹444 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹222 (b) ₹185 (c) ₹37 (d) ₹259
28. 28.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 3 days (c) 17 days (d) 46 days
29. 29.₹165 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹132 (b) ₹133 (c) ₹165 (d) ₹33
30. 30.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 54 days (c) 55 days (d) 5 days
31. 31.If 7 notebooks cost ₹21, how much do 8 notebooks cost? (a) ₹24 (b) ₹168 (c) ₹22 (d) ₹27
32. 32.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 56 days (b) 57 days (c) 20 days (d) 8 days
33. 33.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹24 (b) ₹16 (c) ₹20 (d) ₹8
34. 34.₹275 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹150 (b) ₹25 (c) ₹175 (d) ₹125
35. 35.If 8 mangoes cost ₹112, how much do 3 mangoes cost? (a) ₹107 (b) ₹56 (c) ₹336 (d) ₹42
36. 36.If 3 pens cost ₹45, how much do 4 pens cost? (a) ₹75 (b) ₹180 (c) ₹60 (d) ₹46
37. 37.If 5 mangoes cost ₹105, how much do 7 mangoes cost? (a) ₹107 (b) ₹147 (c) ₹735 (d) ₹168
38. 38.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 2 days (d) 3 days
39. 39.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹19 (b) ₹95 (c) ₹133 (d) ₹114
40. 40.₹490 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹49 (b) ₹245 (c) ₹441 (d) ₹490

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