Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 164 · 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. 1.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 28 days (c) 13 days (d) 3 days
2. 2.₹90 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹9 (b) ₹45 (c) ₹81 (d) ₹90
3. 3.₹120 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹60 (b) ₹90 (c) ₹30 (d) ₹120
4. 4.₹64 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹24 (b) ₹40 (c) ₹32 (d) ₹8
5. 5.8 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 6 days (c) 20 days (d) 5 days
6. 6.If 4 kites cost ₹12, how much do 10 kites cost? (a) ₹18 (b) ₹33 (c) ₹120 (d) ₹30
7. 7.₹301 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹43 (b) ₹301 (c) ₹258 (d) ₹259
8. 8.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 6 days (d) 5 days
9. 9.₹451 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹369 (b) ₹123 (c) ₹41 (d) ₹328
10. 10.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 6 days (c) 18 days (d) 19 days
11. 11.If 5 pens cost ₹15, how much do 8 pens cost? (a) ₹24 (b) ₹27 (c) ₹18 (d) ₹120
12. 12.If 5 mangoes cost ₹90, how much do 7 mangoes cost? (a) ₹144 (b) ₹630 (c) ₹126 (d) ₹92
13. 13.If 6 kites cost ₹90, how much do 2 kites cost? (a) ₹180 (b) ₹30 (c) ₹86 (d) ₹45
14. 14.₹264 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹154 (b) ₹132 (c) ₹22 (d) ₹110
15. 15.₹363 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹33 (b) ₹165 (c) ₹198 (d) ₹231
16. 16.₹130 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹91 (b) ₹65 (c) ₹39 (d) ₹13
17. 17.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 8 days
18. 18.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 7 days (d) 10 days
19. 19.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹105 (b) ₹21 (c) ₹147 (d) ₹126
20. 20.₹403 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹248 (b) ₹279 (c) ₹31 (d) ₹155
21. 21.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 5 days (c) 8 days (d) 20 days
22. 22.₹520 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹260 (b) ₹160 (c) ₹360 (d) ₹40
23. 23.₹319 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹29 (b) ₹145 (c) ₹174 (d) ₹203
24. 24.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 7 days
25. 25.If 9 mangoes cost ₹108, how much do 8 mangoes cost? (a) ₹864 (b) ₹108 (c) ₹96 (d) ₹107
26. 26.₹49 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹35 (b) ₹28 (c) ₹7 (d) ₹21
27. 27.₹350 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹150 (b) ₹175 (c) ₹200 (d) ₹50
28. 28.If 2 mangoes cost ₹18, how much do 7 mangoes cost? (a) ₹72 (b) ₹126 (c) ₹23 (d) ₹63
29. 29.If 9 mangoes cost ₹180, how much do 2 mangoes cost? (a) ₹40 (b) ₹360 (c) ₹60 (d) ₹173
30. 30.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 32 days (d) 33 days
31. 31.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 7 days (c) 53 days (d) 52 days
32. 32.₹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
33. 33.₹322 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹46 (b) ₹138 (c) ₹184 (d) ₹161
34. 34.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 43 days (c) 8 days (d) 42 days
35. 35.If 6 pens cost ₹150, how much do 9 pens cost? (a) ₹225 (b) ₹153 (c) ₹1350 (d) ₹250
36. 36.If 9 pens cost ₹45, how much do 10 pens cost? (a) ₹55 (b) ₹46 (c) ₹50 (d) ₹450
37. 37.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 5 days (d) 16 days
38. 38.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 3 days (d) 4 days
39. 39.₹140 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹10 (b) ₹90 (c) ₹50 (d) ₹70
40. 40.If 7 pens cost ₹147, how much do 2 pens cost? (a) ₹142 (b) ₹63 (c) ₹42 (d) ₹294

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