Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 358 · 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.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹75 (b) ₹90 (c) ₹15 (d) ₹105
2. 2.If 3 notebooks cost ₹72, how much do 6 notebooks cost? (a) ₹144 (b) ₹168 (c) ₹75 (d) ₹432
3. 3.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 4 days (d) 2 days
4. 4.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹112 (b) ₹80 (c) ₹16 (d) ₹96
5. 5.₹296 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹37 (b) ₹111 (c) ₹185 (d) ₹148
6. 6.₹216 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹90 (b) ₹18 (c) ₹126 (d) ₹108
7. 7.If 9 mangoes cost ₹225, how much do 12 mangoes cost? (a) ₹228 (b) ₹2700 (c) ₹325 (d) ₹300
8. 8.If 3 pens cost ₹36, how much do 10 pens cost? (a) ₹360 (b) ₹132 (c) ₹120 (d) ₹43
9. 9.₹276 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹138 (b) ₹115 (c) ₹23 (d) ₹161
10. 10.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 4 days (d) 6 days
11. 11.If 3 kites cost ₹15, how much do 12 kites cost? (a) ₹60 (b) ₹180 (c) ₹24 (d) ₹65
12. 12.₹132 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹72 (b) ₹60 (c) ₹12 (d) ₹66
13. 13.If 6 pens cost ₹84, how much do 11 pens cost? (a) ₹154 (b) ₹89 (c) ₹168 (d) ₹924
14. 14.If 9 mangoes cost ₹180, how much do 5 mangoes cost? (a) ₹176 (b) ₹100 (c) ₹900 (d) ₹120
15. 15.₹322 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹23 (b) ₹161 (c) ₹207 (d) ₹115
16. 16.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 15 days (c) 3 days (d) 27 days
17. 17.₹60 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹25 (b) ₹35 (c) ₹30 (d) ₹5
18. 18.If 8 kites cost ₹80, how much do 9 kites cost? (a) ₹81 (b) ₹90 (c) ₹100 (d) ₹720
19. 19.If 5 pens cost ₹20, how much do 10 pens cost? (a) ₹44 (b) ₹200 (c) ₹40 (d) ₹25
20. 20.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 9 days (d) 25 days
21. 21.3 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
22. 22.₹539 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹49 (b) ₹343 (c) ₹245 (d) ₹294
23. 23.If 4 pens cost ₹52, how much do 12 pens cost? (a) ₹169 (b) ₹156 (c) ₹60 (d) ₹624
24. 24.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 15 days (d) 22 days
25. 25.If 2 mangoes cost ₹12, how much do 3 mangoes cost? (a) ₹36 (b) ₹18 (c) ₹13 (d) ₹24
26. 26.₹30 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹15 (b) ₹30 (c) ₹10 (d) ₹20
27. 27.If 2 pens cost ₹48, how much do 4 pens cost? (a) ₹192 (b) ₹50 (c) ₹96 (d) ₹120
28. 28.If 8 kites cost ₹112, how much do 9 kites cost? (a) ₹1008 (b) ₹140 (c) ₹113 (d) ₹126
29. 29.If 9 mangoes cost ₹171, how much do 4 mangoes cost? (a) ₹166 (b) ₹95 (c) ₹684 (d) ₹76
30. 30.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹45 (b) ₹81 (c) ₹9 (d) ₹72
31. 31.₹315 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹271 (b) ₹315 (c) ₹270 (d) ₹45
32. 32.If 8 notebooks cost ₹168, how much do 6 notebooks cost? (a) ₹126 (b) ₹166 (c) ₹147 (d) ₹1008
33. 33.If 4 kites cost ₹52, how much do 11 kites cost? (a) ₹156 (b) ₹143 (c) ₹572 (d) ₹59
34. 34.If 6 kites cost ₹18, how much do 2 kites cost? (a) ₹6 (b) ₹9 (c) ₹14 (d) ₹36
35. 35.If 2 pens cost ₹50, how much do 7 pens cost? (a) ₹200 (b) ₹55 (c) ₹175 (d) ₹350
36. 36.₹136 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹136 (b) ₹119 (c) ₹68 (d) ₹17
37. 37.If 5 kites cost ₹40, how much do 7 kites cost? (a) ₹64 (b) ₹42 (c) ₹280 (d) ₹56
38. 38.If 2 kites cost ₹10, how much do 4 kites cost? (a) ₹12 (b) ₹20 (c) ₹40 (d) ₹25
39. 39.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 5 days (d) 8 days
40. 40.If 9 kites cost ₹90, how much do 10 kites cost? (a) ₹91 (b) ₹110 (c) ₹100 (d) ₹900

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