Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 564 · 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.If 6 mangoes cost ₹90, how much do 7 mangoes cost? (a) ₹91 (b) ₹630 (c) ₹105 (d) ₹120
2. 2.If 3 notebooks cost ₹12, how much do 10 notebooks cost? (a) ₹120 (b) ₹40 (c) ₹44 (d) ₹19
3. 3.₹209 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹171 (b) ₹19 (c) ₹152 (d) ₹57
4. 4.If 4 kites cost ₹52, how much do 6 kites cost? (a) ₹91 (b) ₹312 (c) ₹54 (d) ₹78
5. 5.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 8 days (d) 6 days
6. 6.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 3 days (d) 1 day
7. 7.₹42 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹18 (b) ₹21 (c) ₹6 (d) ₹24
8. 8.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 16 days (d) 17 days
9. 9.₹200 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹40 (b) ₹160 (c) ₹200 (d) ₹100
10. 10.If 8 kites cost ₹176, how much do 4 kites cost? (a) ₹110 (b) ₹172 (c) ₹704 (d) ₹88
11. 11.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 18 days (c) 10 days (d) 42 days
12. 12.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 29 days (c) 28 days (d) 13 days
13. 13.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 40 days (d) 39 days
14. 14.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 7 days
15. 15.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 26 days (c) 28 days (d) 27 days
16. 16.₹184 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹138 (b) ₹184 (c) ₹46 (d) ₹92
17. 17.If 5 notebooks cost ₹50, how much do 9 notebooks cost? (a) ₹54 (b) ₹450 (c) ₹100 (d) ₹90
18. 18.If 5 mangoes cost ₹25, how much do 7 mangoes cost? (a) ₹175 (b) ₹35 (c) ₹27 (d) ₹40
19. 19.₹273 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹39 (b) ₹156 (c) ₹117 (d) ₹195
20. 20.₹220 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹20 (b) ₹180 (c) ₹110 (d) ₹40
21. 21.If 4 pens cost ₹36, how much do 11 pens cost? (a) ₹99 (b) ₹108 (c) ₹396 (d) ₹43
22. 22.3 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) 6 days (d) 3 days
23. 23.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 7 days (d) 9 days
24. 24.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 11 days (c) 19 days (d) 7 days
25. 25.₹209 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹38 (b) ₹171 (c) ₹19 (d) ₹190
26. 26.If 2 kites cost ₹34, how much do 7 kites cost? (a) ₹119 (b) ₹238 (c) ₹39 (d) ₹136
27. 27.₹377 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹290 (b) ₹261 (c) ₹29 (d) ₹116
28. 28.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 1 day
29. 29.₹220 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹110 (b) ₹160 (c) ₹20 (d) ₹60
30. 30.₹588 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹294 (b) ₹343 (c) ₹245 (d) ₹49
31. 31.If 6 notebooks cost ₹48, how much do 7 notebooks cost? (a) ₹336 (b) ₹64 (c) ₹49 (d) ₹56
32. 32.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 25 days (c) 9 days (d) 13 days
33. 33.₹550 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹50 (b) ₹350 (c) ₹200 (d) ₹275
34. 34.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 4 days (c) 19 days (d) 9 days
35. 35.₹396 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹220 (b) ₹176 (c) ₹198 (d) ₹44
36. 36.₹352 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹32 (b) ₹224 (c) ₹176 (d) ₹128
37. 37.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 16 days (c) 10 days (d) 1 day
38. 38.If 7 mangoes cost ₹49, how much do 4 mangoes cost? (a) ₹196 (b) ₹35 (c) ₹46 (d) ₹28
39. 39.If 4 mangoes cost ₹84, how much do 9 mangoes cost? (a) ₹756 (b) ₹89 (c) ₹210 (d) ₹189
40. 40.If 2 mangoes cost ₹8, how much do 10 mangoes cost? (a) ₹44 (b) ₹80 (c) ₹40 (d) ₹16

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