Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 928 · 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.₹242 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹22 (b) ₹44 (c) ₹198 (d) ₹121
2. 2.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 4 days (c) 9 days (d) 19 days
3. 3.If 7 mangoes cost ₹140, how much do 12 mangoes cost? (a) ₹145 (b) ₹260 (c) ₹240 (d) ₹1680
4. 4.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹64 (b) ₹40 (c) ₹8 (d) ₹52
5. 5.If 9 kites cost ₹216, how much do 11 kites cost? (a) ₹264 (b) ₹2376 (c) ₹288 (d) ₹218
6. 6.₹504 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹210 (b) ₹252 (c) ₹294 (d) ₹42
7. 7.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 27 days (c) 13 days (d) 3 days
8. 8.₹207 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹23 (b) ₹115 (c) ₹138 (d) ₹92
9. 9.7 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) 1 day (d) 6 days
10. 10.₹108 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹54 (b) ₹24 (c) ₹12 (d) ₹84
11. 11.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 1 day (c) 21 days (d) 13 days
12. 12.If 6 kites cost ₹18, how much do 12 kites cost? (a) ₹39 (b) ₹24 (c) ₹36 (d) ₹216
13. 13.₹160 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹60 (b) ₹100 (c) ₹20 (d) ₹80
14. 14.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 11 days
15. 15.If 4 mangoes cost ₹80, how much do 5 mangoes cost? (a) ₹400 (b) ₹100 (c) ₹120 (d) ₹81
16. 16.₹301 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹129 (b) ₹215 (c) ₹43 (d) ₹172
17. 17.₹198 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹108 (b) ₹90 (c) ₹18 (d) ₹99
18. 18.If 3 pens cost ₹15, how much do 4 pens cost? (a) ₹16 (b) ₹25 (c) ₹60 (d) ₹20
19. 19.If 8 kites cost ₹96, how much do 7 kites cost? (a) ₹84 (b) ₹672 (c) ₹95 (d) ₹96
20. 20.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 4 days
21. 21.₹195 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹135 (b) ₹75 (c) ₹120 (d) ₹15
22. 22.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 31 days (b) 30 days (c) 19 days (d) 11 days
23. 23.If 2 pens cost ₹28, how much do 3 pens cost? (a) ₹84 (b) ₹29 (c) ₹56 (d) ₹42
24. 24.₹182 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹70 (b) ₹14 (c) ₹91 (d) ₹112
25. 25.If 9 pens cost ₹45, how much do 11 pens cost? (a) ₹55 (b) ₹495 (c) ₹47 (d) ₹60
26. 26.If 4 notebooks cost ₹20, how much do 8 notebooks cost? (a) ₹24 (b) ₹160 (c) ₹40 (d) ₹45
27. 27.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 17 days (d) 8 days
28. 28.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 7 days (d) 1 day
29. 29.If 5 notebooks cost ₹40, how much do 3 notebooks cost? (a) ₹38 (b) ₹32 (c) ₹120 (d) ₹24
30. 30.If 8 kites cost ₹96, how much do 6 kites cost? (a) ₹576 (b) ₹84 (c) ₹72 (d) ₹94
31. 31.₹77 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹7 (b) ₹14 (c) ₹70 (d) ₹63
32. 32.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 13 days
33. 33.If 6 mangoes cost ₹48, how much do 4 mangoes cost? (a) ₹192 (b) ₹46 (c) ₹32 (d) ₹40
34. 34.If 3 mangoes cost ₹63, how much do 2 mangoes cost? (a) ₹63 (b) ₹126 (c) ₹62 (d) ₹42
35. 35.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 9 days (d) 10 days
36. 36.If 7 pens cost ₹98, how much do 11 pens cost? (a) ₹154 (b) ₹102 (c) ₹1078 (d) ₹168
37. 37.₹45 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹9 (b) ₹18 (c) ₹36 (d) ₹27
38. 38.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 13 days (d) 14 days
39. 39.₹216 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹36 (b) ₹216 (c) ₹108 (d) ₹180
40. 40.If 3 kites cost ₹51, how much do 12 kites cost? (a) ₹612 (b) ₹221 (c) ₹204 (d) ₹60

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