Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 712 · 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 pens cost ₹78, how much do 12 pens cost? (a) ₹84 (b) ₹936 (c) ₹169 (d) ₹156
2. 2.If 7 mangoes cost ₹161, how much do 3 mangoes cost? (a) ₹69 (b) ₹92 (c) ₹483 (d) ₹157
3. 3.If 3 mangoes cost ₹57, how much do 11 mangoes cost? (a) ₹228 (b) ₹209 (c) ₹627 (d) ₹65
4. 4.If 9 notebooks cost ₹108, how much do 10 notebooks cost? (a) ₹132 (b) ₹1080 (c) ₹120 (d) ₹109
5. 5.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 15 days (d) 27 days
6. 6.If 3 pens cost ₹36, how much do 4 pens cost? (a) ₹144 (b) ₹37 (c) ₹60 (d) ₹48
7. 7.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 36 days (c) 4 days (d) 18 days
8. 8.If 3 pens cost ₹39, how much do 4 pens cost? (a) ₹65 (b) ₹52 (c) ₹40 (d) ₹156
9. 9.₹600 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹50 (b) ₹250 (c) ₹300 (d) ₹350
10. 10.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 27 days (c) 26 days (d) 10 days
11. 11.₹99 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹11 (b) ₹89 (c) ₹88 (d) ₹99
12. 12.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 3 days (d) 2 days
13. 13.If 9 mangoes cost ₹171, how much do 4 mangoes cost? (a) ₹95 (b) ₹684 (c) ₹76 (d) ₹166
14. 14.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 6 days (d) 10 days
15. 15.If 6 mangoes cost ₹126, how much do 2 mangoes cost? (a) ₹122 (b) ₹63 (c) ₹252 (d) ₹42
16. 16.If 8 kites cost ₹56, how much do 9 kites cost? (a) ₹70 (b) ₹504 (c) ₹57 (d) ₹63
17. 17.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 2 days (d) 1 day
18. 18.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 1 day (c) 16 days (d) 10 days
19. 19.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹5 (c) ₹10 (d) ₹15
20. 20.If 8 kites cost ₹24, how much do 9 kites cost? (a) ₹25 (b) ₹216 (c) ₹27 (d) ₹30
21. 21.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 18 days (c) 14 days (d) 2 days
22. 22.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 56 days (c) 8 days (d) 20 days
23. 23.If 6 pens cost ₹78, how much do 7 pens cost? (a) ₹91 (b) ₹546 (c) ₹79 (d) ₹104
24. 24.₹52 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹13 (b) ₹39 (c) ₹26 (d) ₹52
25. 25.If 3 mangoes cost ₹48, how much do 10 mangoes cost? (a) ₹160 (b) ₹176 (c) ₹55 (d) ₹480
26. 26.₹104 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹13 (b) ₹91 (c) ₹52 (d) ₹104
27. 27.If 9 pens cost ₹45, how much do 2 pens cost? (a) ₹10 (b) ₹38 (c) ₹90 (d) ₹15
28. 28.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 45 days (c) 3 days (d) 46 days
29. 29.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 13 days (c) 11 days (d) 8 days
30. 30.₹21 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹7 (b) ₹21 (c) ₹15 (d) ₹14
31. 31.₹602 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹215 (b) ₹43 (c) ₹387 (d) ₹301
32. 32.₹56 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹24 (b) ₹28 (c) ₹32 (d) ₹8
33. 33.₹484 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹176 (b) ₹44 (c) ₹308 (d) ₹242
34. 34.₹200 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹60 (b) ₹140 (c) ₹20 (d) ₹100
35. 35.If 3 kites cost ₹42, how much do 4 kites cost? (a) ₹43 (b) ₹56 (c) ₹168 (d) ₹70
36. 36.₹84 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹36 (b) ₹12 (c) ₹48 (d) ₹42
37. 37.If 2 mangoes cost ₹42, how much do 11 mangoes cost? (a) ₹252 (b) ₹231 (c) ₹51 (d) ₹462
38. 38.If 2 kites cost ₹44, how much do 12 kites cost? (a) ₹264 (b) ₹54 (c) ₹528 (d) ₹286
39. 39.If 4 pens cost ₹20, how much do 2 pens cost? (a) ₹10 (b) ₹18 (c) ₹40 (d) ₹15
40. 40.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 13 days (d) 5 days

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