Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 82 · 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.₹91 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹91 (b) ₹79 (c) ₹13 (d) ₹78
2. 2.₹363 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹231 (b) ₹165 (c) ₹33 (d) ₹198
3. 3.₹588 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹378 (b) ₹42 (c) ₹294 (d) ₹210
4. 4.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 7 days (c) 40 days (d) 39 days
5. 5.₹385 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹245 (b) ₹175 (c) ₹210 (d) ₹35
6. 6.If 4 kites cost ₹92, how much do 5 kites cost? (a) ₹460 (b) ₹93 (c) ₹115 (d) ₹138
7. 7.If 8 kites cost ₹128, how much do 11 kites cost? (a) ₹1408 (b) ₹192 (c) ₹176 (d) ₹131
8. 8.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹117 (b) ₹18 (c) ₹72 (d) ₹162
9. 9.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 4 days (c) 3 days (d) 15 days
10. 10.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 7 days (c) 42 days (d) 43 days
11. 11.If 4 kites cost ₹84, how much do 8 kites cost? (a) ₹189 (b) ₹672 (c) ₹88 (d) ₹168
12. 12.If 9 kites cost ₹27, how much do 4 kites cost? (a) ₹22 (b) ₹15 (c) ₹12 (d) ₹108
13. 13.₹205 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹41 (b) ₹164 (c) ₹123 (d) ₹82
14. 14.If 4 kites cost ₹76, how much do 8 kites cost? (a) ₹608 (b) ₹80 (c) ₹171 (d) ₹152
15. 15.₹418 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹38 (b) ₹304 (c) ₹114 (d) ₹209
16. 16.₹75 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹61 (b) ₹15 (c) ₹60 (d) ₹75
17. 17.If 8 pens cost ₹96, how much do 4 pens cost? (a) ₹384 (b) ₹92 (c) ₹60 (d) ₹48
18. 18.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 6 days (c) 24 days (d) 14 days
19. 19.₹81 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹72 (b) ₹9 (c) ₹63 (d) ₹18
20. 20.₹112 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹72 (b) ₹8 (c) ₹40 (d) ₹56
21. 21.If 6 notebooks cost ₹18, how much do 3 notebooks cost? (a) ₹54 (b) ₹9 (c) ₹12 (d) ₹15
22. 22.₹40 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹40 (b) ₹20 (c) ₹5 (d) ₹35
23. 23.₹130 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹65 (b) ₹117 (c) ₹130 (d) ₹13
24. 24.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 5 days (c) 13 days (d) 21 days
25. 25.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 18 days (c) 11 days (d) 19 days
26. 26.If 3 mangoes cost ₹66, how much do 7 mangoes cost? (a) ₹176 (b) ₹70 (c) ₹154 (d) ₹462
27. 27.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 6 days (d) 8 days
28. 28.₹232 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹116 (b) ₹29 (c) ₹145 (d) ₹87
29. 29.If 4 mangoes cost ₹52, how much do 7 mangoes cost? (a) ₹104 (b) ₹91 (c) ₹55 (d) ₹364
30. 30.₹507 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹390 (b) ₹39 (c) ₹351 (d) ₹156
31. 31.If 4 kites cost ₹72, how much do 5 kites cost? (a) ₹360 (b) ₹108 (c) ₹90 (d) ₹73
32. 32.If 5 notebooks cost ₹45, how much do 4 notebooks cost? (a) ₹45 (b) ₹44 (c) ₹36 (d) ₹180
33. 33.₹588 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹294 (b) ₹49 (c) ₹245 (d) ₹343
34. 34.If 7 kites cost ₹98, how much do 3 kites cost? (a) ₹294 (b) ₹56 (c) ₹94 (d) ₹42
35. 35.If 4 pens cost ₹60, how much do 10 pens cost? (a) ₹600 (b) ₹66 (c) ₹165 (d) ₹150
36. 36.If 7 kites cost ₹84, how much do 4 kites cost? (a) ₹81 (b) ₹336 (c) ₹60 (d) ₹48
37. 37.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 14 days (b) 6 days (c) 5 days (d) 20 days
38. 38.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 23 days (c) 14 days (d) 22 days
39. 39.₹48 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹24 (b) ₹48 (c) ₹16 (d) ₹32
40. 40.₹297 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹81 (b) ₹243 (c) ₹216 (d) ₹27

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