Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 662 · 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 ₹60, how much do 10 pens cost? (a) ₹600 (b) ₹64 (c) ₹110 (d) ₹100
2. 2.If 9 pens cost ₹63, how much do 3 pens cost? (a) ₹57 (b) ₹28 (c) ₹21 (d) ₹189
3. 3.₹70 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹70 (b) ₹35 (c) ₹14 (d) ₹56
4. 4.If 3 kites cost ₹39, how much do 4 kites cost? (a) ₹52 (b) ₹65 (c) ₹40 (d) ₹156
5. 5.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 9 days (d) 7 days
6. 6.If 3 mangoes cost ₹24, how much do 9 mangoes cost? (a) ₹72 (b) ₹216 (c) ₹80 (d) ₹30
7. 7.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 17 days (d) 9 days
8. 8.₹396 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹36 (b) ₹72 (c) ₹198 (d) ₹324
9. 9.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 21 days (c) 22 days (d) 11 days
10. 10.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 18 days (b) 14 days (c) 3 days (d) 2 days
11. 11.₹198 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹99 (b) ₹176 (c) ₹198 (d) ₹22
12. 12.₹637 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹245 (b) ₹441 (c) ₹392 (d) ₹49
13. 13.₹63 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹14 (b) ₹7 (c) ₹56 (d) ₹49
14. 14.If 9 notebooks cost ₹81, how much do 4 notebooks cost? (a) ₹36 (b) ₹324 (c) ₹45 (d) ₹76
15. 15.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 12 days (c) 7 days (d) 8 days
16. 16.₹68 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹17 (b) ₹34 (c) ₹68 (d) ₹51
17. 17.₹403 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹124 (b) ₹31 (c) ₹279 (d) ₹310
18. 18.₹126 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹90 (b) ₹63 (c) ₹18 (d) ₹36
19. 19.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 45 days (b) 21 days (c) 5 days (d) 9 days
20. 20.₹154 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹84 (b) ₹77 (c) ₹14 (d) ₹70
21. 21.₹297 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹189 (b) ₹216 (c) ₹27 (d) ₹108
22. 22.₹585 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹450 (b) ₹45 (c) ₹180 (d) ₹405
23. 23.If 8 mangoes cost ₹48, how much do 12 mangoes cost? (a) ₹576 (b) ₹72 (c) ₹78 (d) ₹52
24. 24.If 5 kites cost ₹70, how much do 2 kites cost? (a) ₹140 (b) ₹42 (c) ₹28 (d) ₹67
25. 25.₹135 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹15 (b) ₹135 (c) ₹121 (d) ₹120
26. 26.₹165 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹105 (b) ₹120 (c) ₹15 (d) ₹60
27. 27.If 8 mangoes cost ₹96, how much do 11 mangoes cost? (a) ₹144 (b) ₹99 (c) ₹1056 (d) ₹132
28. 28.If 2 mangoes cost ₹6, how much do 3 mangoes cost? (a) ₹12 (b) ₹7 (c) ₹9 (d) ₹18
29. 29.₹93 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹31 (b) ₹62 (c) ₹93 (d) ₹63
30. 30.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 2 days (d) 5 days
31. 31.₹559 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹43 (b) ₹344 (c) ₹215 (d) ₹387
32. 32.If 8 mangoes cost ₹72, how much do 5 mangoes cost? (a) ₹54 (b) ₹69 (c) ₹360 (d) ₹45
33. 33.If 5 mangoes cost ₹20, how much do 4 mangoes cost? (a) ₹80 (b) ₹20 (c) ₹19 (d) ₹16
34. 34.If 3 kites cost ₹12, how much do 5 kites cost? (a) ₹24 (b) ₹60 (c) ₹14 (d) ₹20
35. 35.If 4 kites cost ₹32, how much do 5 kites cost? (a) ₹48 (b) ₹33 (c) ₹40 (d) ₹160
36. 36.If 4 mangoes cost ₹40, how much do 6 mangoes cost? (a) ₹42 (b) ₹60 (c) ₹240 (d) ₹70
37. 37.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 12 days (d) 9 days
38. 38.₹50 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹25 (b) ₹5 (c) ₹45 (d) ₹50
39. 39.₹288 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹120 (b) ₹168 (c) ₹144 (d) ₹24
40. 40.₹144 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹72 (b) ₹16 (c) ₹112 (d) ₹32

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