Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 148 · 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.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹91 (b) ₹78 (c) ₹13 (d) ₹65
2. 2.₹150 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹50 (b) ₹75 (c) ₹150 (d) ₹100
3. 3.If 6 pens cost ₹96, how much do 2 pens cost? (a) ₹32 (b) ₹192 (c) ₹92 (d) ₹48
4. 4.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 7 days (d) 9 days
5. 5.If 4 kites cost ₹88, how much do 7 kites cost? (a) ₹616 (b) ₹154 (c) ₹91 (d) ₹176
6. 6.If 5 pens cost ₹20, how much do 10 pens cost? (a) ₹25 (b) ₹44 (c) ₹200 (d) ₹40
7. 7.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 8 days (c) 18 days (d) 11 days
8. 8.If 8 notebooks cost ₹184, how much do 9 notebooks cost? (a) ₹185 (b) ₹207 (c) ₹230 (d) ₹1656
9. 9.₹492 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹287 (b) ₹41 (c) ₹205 (d) ₹246
10. 10.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 6 days (d) 8 days
11. 11.₹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
12. 12.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 18 days (c) 7 days (d) 10 days
13. 13.If 9 mangoes cost ₹99, how much do 6 mangoes cost? (a) ₹77 (b) ₹66 (c) ₹96 (d) ₹594
14. 14.If 9 kites cost ₹108, how much do 11 kites cost? (a) ₹144 (b) ₹110 (c) ₹132 (d) ₹1188
15. 15.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 18 days (c) 11 days (d) 17 days
16. 16.If 2 kites cost ₹50, how much do 10 kites cost? (a) ₹58 (b) ₹275 (c) ₹250 (d) ₹500
17. 17.If 6 pens cost ₹102, how much do 12 pens cost? (a) ₹204 (b) ₹221 (c) ₹1224 (d) ₹108
18. 18.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 7 days (d) 8 days
19. 19.If 2 pens cost ₹6, how much do 8 pens cost? (a) ₹27 (b) ₹48 (c) ₹24 (d) ₹12
20. 20.If 5 kites cost ₹100, how much do 7 kites cost? (a) ₹140 (b) ₹102 (c) ₹700 (d) ₹160
21. 21.₹72 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹36 (b) ₹6 (c) ₹42 (d) ₹30
22. 22.If 8 kites cost ₹136, how much do 11 kites cost? (a) ₹1496 (b) ₹204 (c) ₹139 (d) ₹187
23. 23.₹66 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹55 (b) ₹11 (c) ₹66 (d) ₹33
24. 24.If 2 pens cost ₹26, how much do 9 pens cost? (a) ₹130 (b) ₹234 (c) ₹117 (d) ₹33
25. 25.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 34 days (d) 33 days
26. 26.If 6 pens cost ₹150, how much do 2 pens cost? (a) ₹146 (b) ₹300 (c) ₹50 (d) ₹75
27. 27.If 9 pens cost ₹36, how much do 10 pens cost? (a) ₹40 (b) ₹360 (c) ₹44 (d) ₹37
28. 28.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 4 days (c) 6 days (d) 36 days
29. 29.₹184 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹92 (b) ₹23 (c) ₹69 (d) ₹115
30. 30.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹7 (b) ₹14 (c) ₹21 (d) ₹28
31. 31.If 3 kites cost ₹54, how much do 7 kites cost? (a) ₹58 (b) ₹144 (c) ₹378 (d) ₹126
32. 32.If 4 mangoes cost ₹84, how much do 5 mangoes cost? (a) ₹126 (b) ₹105 (c) ₹85 (d) ₹420
33. 33.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 3 days (d) 12 days
34. 34.₹384 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹32 (b) ₹160 (c) ₹224 (d) ₹192
35. 35.If 4 kites cost ₹84, how much do 12 kites cost? (a) ₹1008 (b) ₹92 (c) ₹252 (d) ₹273
36. 36.If 2 pens cost ₹14, how much do 3 pens cost? (a) ₹15 (b) ₹21 (c) ₹28 (d) ₹42
37. 37.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹16 (b) ₹80 (c) ₹64 (d) ₹72
38. 38.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 6 days (d) 12 days
39. 39.If 2 kites cost ₹30, how much do 8 kites cost? (a) ₹36 (b) ₹120 (c) ₹135 (d) ₹240
40. 40.₹72 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹8 (b) ₹36 (c) ₹72 (d) ₹64

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