Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 351 · 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 7 pens cost ₹21, how much do 8 pens cost? (a) ₹22 (b) ₹24 (c) ₹168 (d) ₹27
2. 2.If 6 pens cost ₹126, how much do 2 pens cost? (a) ₹252 (b) ₹122 (c) ₹63 (d) ₹42
3. 3.₹252 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹126 (b) ₹140 (c) ₹112 (d) ₹28
4. 4.7 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) 21 days (d) 22 days
5. 5.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 1 day (d) 10 days
6. 6.₹225 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹225 (b) ₹181 (c) ₹180 (d) ₹45
7. 7.₹198 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹99 (b) ₹88 (c) ₹110 (d) ₹22
8. 8.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 7 days (d) 4 days
9. 9.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 13 days (d) 25 days
10. 10.₹286 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹143 (b) ₹208 (c) ₹26 (d) ₹78
11. 11.₹198 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹18 (b) ₹99 (c) ₹126 (d) ₹72
12. 12.If 8 pens cost ₹136, how much do 9 pens cost? (a) ₹1224 (b) ₹137 (c) ₹153 (d) ₹170
13. 13.If 8 mangoes cost ₹104, how much do 3 mangoes cost? (a) ₹312 (b) ₹39 (c) ₹99 (d) ₹52
14. 14.₹282 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹141 (b) ₹282 (c) ₹235 (d) ₹47
15. 15.If 5 mangoes cost ₹80, how much do 4 mangoes cost? (a) ₹80 (b) ₹64 (c) ₹320 (d) ₹79
16. 16.If 6 pens cost ₹150, how much do 4 pens cost? (a) ₹125 (b) ₹148 (c) ₹100 (d) ₹600
17. 17.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 2 days
18. 18.If 9 pens cost ₹63, how much do 12 pens cost? (a) ₹66 (b) ₹756 (c) ₹84 (d) ₹91
19. 19.If 7 pens cost ₹126, how much do 5 pens cost? (a) ₹630 (b) ₹108 (c) ₹90 (d) ₹124
20. 20.If 2 kites cost ₹26, how much do 4 kites cost? (a) ₹104 (b) ₹65 (c) ₹52 (d) ₹28
21. 21.₹559 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹387 (b) ₹43 (c) ₹344 (d) ₹215
22. 22.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 1 day (d) 9 days
23. 23.If 3 mangoes cost ₹15, how much do 8 mangoes cost? (a) ₹45 (b) ₹120 (c) ₹20 (d) ₹40
24. 24.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 3 days (c) 27 days (d) 15 days
25. 25.If 6 pens cost ₹30, how much do 11 pens cost? (a) ₹330 (b) ₹60 (c) ₹55 (d) ₹35
26. 26.If 8 pens cost ₹32, how much do 3 pens cost? (a) ₹16 (b) ₹12 (c) ₹27 (d) ₹96
27. 27.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 2 days (d) 8 days
28. 28.If 2 pens cost ₹44, how much do 4 pens cost? (a) ₹176 (b) ₹110 (c) ₹46 (d) ₹88
29. 29.₹360 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹40 (b) ₹180 (c) ₹160 (d) ₹200
30. 30.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 35 days (c) 19 days (d) 36 days
31. 31.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 45 days (c) 9 days (d) 5 days
32. 32.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 22 days (b) 12 days (c) 21 days (d) 16 days
33. 33.If 6 kites cost ₹138, how much do 12 kites cost? (a) ₹1656 (b) ₹276 (c) ₹299 (d) ₹144
34. 34.₹190 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹95 (b) ₹76 (c) ₹38 (d) ₹114
35. 35.₹96 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹32 (b) ₹48 (c) ₹64 (d) ₹96
36. 36.₹385 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹175 (b) ₹245 (c) ₹210 (d) ₹35
37. 37.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 12 days (d) 4 days
38. 38.₹306 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹34 (b) ₹136 (c) ₹170 (d) ₹153
39. 39.If 4 notebooks cost ₹92, how much do 2 notebooks cost? (a) ₹46 (b) ₹69 (c) ₹184 (d) ₹90
40. 40.₹416 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹128 (b) ₹32 (c) ₹288 (d) ₹208

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