Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 143 · 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.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹12 (b) ₹15 (c) ₹18 (d) ₹6
2. 2.₹341 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹217 (b) ₹248 (c) ₹31 (d) ₹124
3. 3.₹266 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹133 (b) ₹38 (c) ₹114 (d) ₹152
4. 4.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 21 days (c) 22 days (d) 12 days
5. 5.₹260 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹20 (b) ₹100 (c) ₹160 (d) ₹130
6. 6.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 28 days (b) 11 days (c) 17 days (d) 7 days
7. 7.₹429 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹195 (b) ₹273 (c) ₹39 (d) ₹234
8. 8.₹235 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹141 (b) ₹94 (c) ₹47 (d) ₹188
9. 9.₹200 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹100 (b) ₹20 (c) ₹60 (d) ₹140
10. 10.If 7 mangoes cost ₹77, how much do 8 mangoes cost? (a) ₹99 (b) ₹78 (c) ₹616 (d) ₹88
11. 11.₹184 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹92 (b) ₹69 (c) ₹23 (d) ₹115
12. 12.₹56 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹48 (b) ₹8 (c) ₹28 (d) ₹56
13. 13.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 14 days (c) 10 days (d) 6 days
14. 14.If 6 pens cost ₹18, how much do 11 pens cost? (a) ₹23 (b) ₹198 (c) ₹33 (d) ₹36
15. 15.₹112 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹56 (b) ₹112 (c) ₹84 (d) ₹28
16. 16.₹161 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹23 (b) ₹69 (c) ₹115 (d) ₹92
17. 17.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 8 days (d) 9 days
18. 18.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 17 days (c) 3 days (d) 32 days
19. 19.₹96 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹48 (b) ₹96 (c) ₹80 (d) ₹16
20. 20.₹546 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹351 (b) ₹39 (c) ₹195 (d) ₹273
21. 21.₹200 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹120 (b) ₹100 (c) ₹80 (d) ₹40
22. 22.If 3 pens cost ₹36, how much do 8 pens cost? (a) ₹288 (b) ₹108 (c) ₹96 (d) ₹41
23. 23.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 10 days (d) 5 days
24. 24.₹220 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹20 (b) ₹80 (c) ₹140 (d) ₹110
25. 25.₹238 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹119 (b) ₹68 (c) ₹34 (d) ₹170
26. 26.If 2 kites cost ₹6, how much do 4 kites cost? (a) ₹8 (b) ₹24 (c) ₹15 (d) ₹12
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) 8 days (c) 7 days (d) 2 days
28. 28.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 17 days (d) 4 days
29. 29.If 5 pens cost ₹15, how much do 4 pens cost? (a) ₹60 (b) ₹12 (c) ₹14 (d) ₹15
30. 30.If 2 pens cost ₹6, how much do 9 pens cost? (a) ₹13 (b) ₹54 (c) ₹27 (d) ₹30
31. 31.₹286 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹26 (b) ₹143 (c) ₹130 (d) ₹156
32. 32.₹390 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹30 (b) ₹120 (c) ₹195 (d) ₹270
33. 33.If 4 notebooks cost ₹76, how much do 6 notebooks cost? (a) ₹114 (b) ₹78 (c) ₹456 (d) ₹133
34. 34.₹182 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹26 (b) ₹182 (c) ₹91 (d) ₹156
35. 35.If 4 notebooks cost ₹16, how much do 5 notebooks cost? (a) ₹17 (b) ₹24 (c) ₹20 (d) ₹80
36. 36.5 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 11 days (d) 10 days
37. 37.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 57 days (c) 56 days (d) 20 days
38. 38.₹63 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹14 (b) ₹7 (c) ₹56 (d) ₹49
39. 39.₹588 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹294 (b) ₹49 (c) ₹343 (d) ₹245
40. 40.If 6 notebooks cost ₹78, how much do 12 notebooks cost? (a) ₹156 (b) ₹169 (c) ₹936 (d) ₹84

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