Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 631 · 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.₹96 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹24 (b) ₹96 (c) ₹48 (d) ₹72
2. 2.If 9 pens cost ₹189, how much do 2 pens cost? (a) ₹42 (b) ₹378 (c) ₹63 (d) ₹182
3. 3.₹637 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹392 (b) ₹245 (c) ₹441 (d) ₹49
4. 4.₹576 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹336 (b) ₹240 (c) ₹48 (d) ₹288
5. 5.If 5 pens cost ₹35, how much do 10 pens cost? (a) ₹77 (b) ₹40 (c) ₹350 (d) ₹70
6. 6.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 21 days (d) 9 days
7. 7.If 5 mangoes cost ₹25, how much do 3 mangoes cost? (a) ₹15 (b) ₹23 (c) ₹20 (d) ₹75
8. 8.If 6 notebooks cost ₹42, how much do 12 notebooks cost? (a) ₹84 (b) ₹504 (c) ₹48 (d) ₹91
9. 9.If 2 notebooks cost ₹36, how much do 6 notebooks cost? (a) ₹40 (b) ₹126 (c) ₹216 (d) ₹108
10. 10.If 6 pens cost ₹18, how much do 10 pens cost? (a) ₹22 (b) ₹33 (c) ₹180 (d) ₹30
11. 11.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 4 days (d) 6 days
12. 12.If 9 notebooks cost ₹90, how much do 5 notebooks cost? (a) ₹450 (b) ₹60 (c) ₹86 (d) ₹50
13. 13.If 9 notebooks cost ₹36, how much do 4 notebooks cost? (a) ₹144 (b) ₹31 (c) ₹20 (d) ₹16
14. 14.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 5 days (d) 7 days
15. 15.If 6 notebooks cost ₹30, how much do 7 notebooks cost? (a) ₹210 (b) ₹31 (c) ₹40 (d) ₹35
16. 16.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹25 (b) ₹40 (c) ₹45 (d) ₹5
17. 17.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 4 days (d) 3 days
18. 18.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 5 days (d) 13 days
19. 19.If 7 pens cost ₹119, how much do 3 pens cost? (a) ₹68 (b) ₹51 (c) ₹357 (d) ₹115
20. 20.If 2 mangoes cost ₹8, how much do 4 mangoes cost? (a) ₹20 (b) ₹16 (c) ₹10 (d) ₹32
21. 21.₹65 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹20 (b) ₹50 (c) ₹45 (d) ₹5
22. 22.If 7 pens cost ₹28, how much do 4 pens cost? (a) ₹112 (b) ₹20 (c) ₹16 (d) ₹25
23. 23.If 3 pens cost ₹63, how much do 4 pens cost? (a) ₹105 (b) ₹84 (c) ₹252 (d) ₹64
24. 24.If 2 kites cost ₹14, how much do 6 kites cost? (a) ₹49 (b) ₹42 (c) ₹18 (d) ₹84
25. 25.If 2 pens cost ₹14, how much do 3 pens cost? (a) ₹28 (b) ₹42 (c) ₹15 (d) ₹21
26. 26.₹121 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹110 (b) ₹11 (c) ₹22 (d) ₹99
27. 27.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 18 days (c) 12 days (d) 19 days
28. 28.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 14 days (d) 9 days
29. 29.₹108 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹108 (b) ₹54 (c) ₹90 (d) ₹18
30. 30.₹145 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹87 (b) ₹29 (c) ₹58 (d) ₹116
31. 31.If 4 kites cost ₹100, how much do 8 kites cost? (a) ₹800 (b) ₹104 (c) ₹225 (d) ₹200
32. 32.If 7 kites cost ₹77, how much do 11 kites cost? (a) ₹132 (b) ₹847 (c) ₹121 (d) ₹81
33. 33.₹64 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹56 (b) ₹8 (c) ₹64 (d) ₹32
34. 34.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 21 days (d) 15 days
35. 35.₹286 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹143 (b) ₹156 (c) ₹130 (d) ₹26
36. 36.If 6 pens cost ₹90, how much do 4 pens cost? (a) ₹360 (b) ₹75 (c) ₹60 (d) ₹88
37. 37.If 2 mangoes cost ₹22, how much do 10 mangoes cost? (a) ₹220 (b) ₹121 (c) ₹30 (d) ₹110
38. 38.If 7 kites cost ₹84, how much do 8 kites cost? (a) ₹85 (b) ₹672 (c) ₹96 (d) ₹108
39. 39.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 26 days (c) 13 days (d) 27 days
40. 40.₹330 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹30 (b) ₹165 (c) ₹60 (d) ₹270

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