Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 240 · 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.₹176 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹32 (b) ₹144 (c) ₹16 (d) ₹88
2. 2.If 5 pens cost ₹70, how much do 6 pens cost? (a) ₹98 (b) ₹71 (c) ₹84 (d) ₹420
3. 3.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 7 days (d) 6 days
4. 4.₹120 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹60 (b) ₹40 (c) ₹80 (d) ₹120
5. 5.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 17 days (d) 25 days
6. 6.₹294 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹294 (b) ₹49 (c) ₹147 (d) ₹245
7. 7.If 3 notebooks cost ₹39, how much do 4 notebooks cost? (a) ₹40 (b) ₹156 (c) ₹65 (d) ₹52
8. 8.₹546 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹273 (b) ₹378 (c) ₹42 (d) ₹168
9. 9.₹410 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹123 (b) ₹41 (c) ₹287 (d) ₹205
10. 10.If 6 mangoes cost ₹42, how much do 8 mangoes cost? (a) ₹56 (b) ₹336 (c) ₹63 (d) ₹44
11. 11.If 4 kites cost ₹64, how much do 2 kites cost? (a) ₹128 (b) ₹62 (c) ₹32 (d) ₹48
12. 12.If 7 mangoes cost ₹49, how much do 8 mangoes cost? (a) ₹50 (b) ₹56 (c) ₹63 (d) ₹392
13. 13.If 8 notebooks cost ₹128, how much do 3 notebooks cost? (a) ₹384 (b) ₹123 (c) ₹64 (d) ₹48
14. 14.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 13 days (d) 12 days
15. 15.₹374 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹187 (b) ₹170 (c) ₹34 (d) ₹204
16. 16.5 workers can build a wall in 12 days. How many days will 10 workers take, working at the same speed? (a) 24 days (b) 6 days (c) 7 days (d) 17 days
17. 17.3 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
18. 18.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 7 days (d) 3 days
19. 19.₹99 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹63 (b) ₹36 (c) ₹9 (d) ₹72
20. 20.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 9 days (c) 15 days (d) 13 days
21. 21.₹154 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹154 (b) ₹132 (c) ₹22 (d) ₹77
22. 22.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹80 (b) ₹16 (c) ₹72 (d) ₹64
23. 23.If 3 kites cost ₹27, how much do 8 kites cost? (a) ₹72 (b) ₹81 (c) ₹216 (d) ₹32
24. 24.₹104 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹78 (b) ₹52 (c) ₹104 (d) ₹26
25. 25.₹144 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹144 (b) ₹108 (c) ₹72 (d) ₹36
26. 26.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹16 (c) ₹8 (d) ₹24
27. 27.₹180 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹20 (b) ₹140 (c) ₹90 (d) ₹40
28. 28.If 4 pens cost ₹44, how much do 12 pens cost? (a) ₹528 (b) ₹143 (c) ₹132 (d) ₹52
29. 29.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 16 days (d) 15 days
30. 30.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 17 days (d) 13 days
31. 31.₹60 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹35 (b) ₹30 (c) ₹25 (d) ₹5
32. 32.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 9 days (d) 14 days
33. 33.₹322 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹115 (b) ₹161 (c) ₹23 (d) ₹207
34. 34.₹125 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹100 (b) ₹75 (c) ₹50 (d) ₹25
35. 35.If 9 notebooks cost ₹144, how much do 11 notebooks cost? (a) ₹1584 (b) ₹146 (c) ₹176 (d) ₹192
36. 36.₹187 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹153 (b) ₹34 (c) ₹170 (d) ₹17
37. 37.If 7 notebooks cost ₹21, how much do 6 notebooks cost? (a) ₹21 (b) ₹126 (c) ₹20 (d) ₹18
38. 38.₹153 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹17 (b) ₹119 (c) ₹34 (d) ₹136
39. 39.₹473 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹129 (b) ₹43 (c) ₹387 (d) ₹344
40. 40.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹55 (b) ₹44 (c) ₹66 (d) ₹11

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