Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 713 · 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 5 notebooks cost ₹70, how much do 7 notebooks cost? (a) ₹490 (b) ₹72 (c) ₹112 (d) ₹98
2. 2.If 2 notebooks cost ₹12, how much do 3 notebooks cost? (a) ₹24 (b) ₹18 (c) ₹36 (d) ₹13
3. 3.If 5 pens cost ₹15, how much do 3 pens cost? (a) ₹45 (b) ₹12 (c) ₹9 (d) ₹13
4. 4.₹210 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹42 (b) ₹105 (c) ₹84 (d) ₹126
5. 5.₹258 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹43 (b) ₹129 (c) ₹258 (d) ₹215
6. 6.If 7 kites cost ₹63, how much do 2 kites cost? (a) ₹18 (b) ₹27 (c) ₹58 (d) ₹126
7. 7.If 6 pens cost ₹42, how much do 9 pens cost? (a) ₹45 (b) ₹70 (c) ₹378 (d) ₹63
8. 8.If 8 pens cost ₹72, how much do 3 pens cost? (a) ₹216 (b) ₹27 (c) ₹67 (d) ₹36
9. 9.If 2 kites cost ₹26, how much do 12 kites cost? (a) ₹156 (b) ₹312 (c) ₹169 (d) ₹36
10. 10.₹539 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹196 (b) ₹49 (c) ₹343 (d) ₹392
11. 11.₹301 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹258 (b) ₹43 (c) ₹215 (d) ₹86
12. 12.8 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
13. 13.₹484 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹88 (b) ₹242 (c) ₹44 (d) ₹396
14. 14.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 9 days (d) 3 days
15. 15.If 3 mangoes cost ₹72, how much do 4 mangoes cost? (a) ₹73 (b) ₹96 (c) ₹120 (d) ₹288
16. 16.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 6 days (d) 7 days
17. 17.₹364 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹234 (b) ₹130 (c) ₹182 (d) ₹26
18. 18.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 2 days (c) 14 days (d) 24 days
19. 19.If 2 notebooks cost ₹32, how much do 7 notebooks cost? (a) ₹37 (b) ₹128 (c) ₹224 (d) ₹112
20. 20.If 8 kites cost ₹160, how much do 9 kites cost? (a) ₹161 (b) ₹180 (c) ₹1440 (d) ₹200
21. 21.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 26 days (c) 27 days (d) 11 days
22. 22.If 3 pens cost ₹63, how much do 12 pens cost? (a) ₹72 (b) ₹756 (c) ₹252 (d) ₹273
23. 23.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹84 (b) ₹108 (c) ₹60 (d) ₹12
24. 24.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹234 (b) ₹156 (c) ₹39 (d) ₹195
25. 25.₹384 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹48 (b) ₹144 (c) ₹192 (d) ₹240
26. 26.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 2 days (c) 13 days (d) 1 day
27. 27.₹322 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹161 (b) ₹92 (c) ₹230 (d) ₹46
28. 28.If 5 kites cost ₹30, how much do 4 kites cost? (a) ₹24 (b) ₹30 (c) ₹120 (d) ₹29
29. 29.₹120 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹40 (b) ₹60 (c) ₹80 (d) ₹120
30. 30.If 7 pens cost ₹105, how much do 10 pens cost? (a) ₹150 (b) ₹108 (c) ₹165 (d) ₹1050
31. 31.9 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 11 days (d) 12 days
32. 32.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 27 days (d) 13 days
33. 33.₹220 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹80 (b) ₹110 (c) ₹20 (d) ₹140
34. 34.₹287 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹41 (b) ₹82 (c) ₹205 (d) ₹246
35. 35.₹98 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹28 (b) ₹14 (c) ₹49 (d) ₹70
36. 36.If 2 mangoes cost ₹6, how much do 7 mangoes cost? (a) ₹21 (b) ₹24 (c) ₹11 (d) ₹42
37. 37.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹133 (b) ₹19 (c) ₹114 (d) ₹95
38. 38.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 5 days
39. 39.₹54 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹45 (b) ₹9 (c) ₹54 (d) ₹27
40. 40.₹132 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹60 (b) ₹72 (c) ₹66 (d) ₹12

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