Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 296 · 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. 1.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 3 days
2. 2.If 5 kites cost ₹100, how much do 6 kites cost? (a) ₹101 (b) ₹140 (c) ₹600 (d) ₹120
3. 3.₹297 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹165 (b) ₹132 (c) ₹198 (d) ₹33
4. 4.₹360 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹40 (b) ₹160 (c) ₹180 (d) ₹200
5. 5.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 1 day (c) 16 days (d) 13 days
6. 6.If 7 mangoes cost ₹119, how much do 4 mangoes cost? (a) ₹68 (b) ₹85 (c) ₹116 (d) ₹476
7. 7.₹78 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹39 (b) ₹30 (c) ₹6 (d) ₹48
8. 8.If 9 pens cost ₹180, how much do 11 pens cost? (a) ₹1980 (b) ₹240 (c) ₹220 (d) ₹182
9. 9.If 5 pens cost ₹105, how much do 11 pens cost? (a) ₹111 (b) ₹252 (c) ₹231 (d) ₹1155
10. 10.₹114 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹57 (b) ₹38 (c) ₹114 (d) ₹76
11. 11.If 7 pens cost ₹168, how much do 8 pens cost? (a) ₹216 (b) ₹192 (c) ₹1344 (d) ₹169
12. 12.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 2 days
13. 13.₹147 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹63 (b) ₹105 (c) ₹84 (d) ₹21
14. 14.If 2 kites cost ₹28, how much do 3 kites cost? (a) ₹56 (b) ₹84 (c) ₹29 (d) ₹42
15. 15.₹130 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹117 (b) ₹65 (c) ₹13 (d) ₹130
16. 16.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 56 days (b) 8 days (c) 57 days (d) 20 days
17. 17.If 2 mangoes cost ₹44, how much do 7 mangoes cost? (a) ₹308 (b) ₹154 (c) ₹176 (d) ₹49
18. 18.6 workers can build a wall in 14 days. How many days will 12 workers take, working at the same speed? (a) 20 days (b) 28 days (c) 7 days (d) 8 days
19. 19.₹81 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹81 (b) ₹73 (c) ₹9 (d) ₹72
20. 20.₹238 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹119 (b) ₹204 (c) ₹238 (d) ₹34
21. 21.If 8 pens cost ₹128, how much do 12 pens cost? (a) ₹208 (b) ₹132 (c) ₹192 (d) ₹1536
22. 22.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 23 days (b) 7 days (c) 22 days (d) 15 days
23. 23.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 9 days (d) 2 days
24. 24.8 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 18 days (b) 25 days (c) 12 days (d) 24 days
25. 25.If 3 mangoes cost ₹24, how much do 4 mangoes cost? (a) ₹32 (b) ₹40 (c) ₹96 (d) ₹25
26. 26.If 9 notebooks cost ₹27, how much do 6 notebooks cost? (a) ₹18 (b) ₹24 (c) ₹21 (d) ₹162
27. 27.₹322 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹115 (b) ₹23 (c) ₹207 (d) ₹161
28. 28.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 5 days (d) 6 days
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.₹320 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹32 (b) ₹288 (c) ₹320 (d) ₹160
31. 31.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 1 day (d) 10 days
32. 32.If 8 kites cost ₹96, how much do 3 kites cost? (a) ₹48 (b) ₹36 (c) ₹288 (d) ₹91
33. 33.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 11 days (d) 9 days
34. 34.₹333 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹37 (b) ₹74 (c) ₹259 (d) ₹296
35. 35.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 9 days (d) 4 days
36. 36.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 13 days (d) 5 days
37. 37.If 2 kites cost ₹14, how much do 3 kites cost? (a) ₹15 (b) ₹28 (c) ₹21 (d) ₹42
38. 38.₹484 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹132 (b) ₹352 (c) ₹44 (d) ₹242
39. 39.If 8 mangoes cost ₹88, how much do 2 mangoes cost? (a) ₹22 (b) ₹176 (c) ₹33 (d) ₹82
40. 40.₹455 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹315 (b) ₹140 (c) ₹350 (d) ₹35

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