Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 181 · 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. 1.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 5 days (c) 55 days (d) 54 days
2. 2.₹392 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹343 (b) ₹392 (c) ₹196 (d) ₹49
3. 3.If 2 kites cost ₹42, how much do 4 kites cost? (a) ₹44 (b) ₹105 (c) ₹168 (d) ₹84
4. 4.If 5 pens cost ₹80, how much do 4 pens cost? (a) ₹80 (b) ₹320 (c) ₹64 (d) ₹79
5. 5.If 6 notebooks cost ₹66, how much do 11 notebooks cost? (a) ₹71 (b) ₹726 (c) ₹132 (d) ₹121
6. 6.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 5 days (d) 8 days
7. 7.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 16 days (c) 4 days (d) 36 days
8. 8.If 6 notebooks cost ₹138, how much do 4 notebooks cost? (a) ₹115 (b) ₹136 (c) ₹92 (d) ₹552
9. 9.If 9 pens cost ₹225, how much do 2 pens cost? (a) ₹218 (b) ₹50 (c) ₹75 (d) ₹450
10. 10.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 26 days (b) 9 days (c) 17 days (d) 27 days
11. 11.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 31 days (b) 11 days (c) 30 days (d) 19 days
12. 12.₹470 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹235 (b) ₹141 (c) ₹47 (d) ₹329
13. 13.₹95 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹77 (b) ₹76 (c) ₹19 (d) ₹95
14. 14.₹140 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹140 (b) ₹70 (c) ₹20 (d) ₹120
15. 15.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 8 days (c) 7 days (d) 6 days
16. 16.If 6 mangoes cost ₹144, how much do 9 mangoes cost? (a) ₹1296 (b) ₹240 (c) ₹216 (d) ₹147
17. 17.₹154 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹77 (b) ₹14 (c) ₹70 (d) ₹84
18. 18.If 5 pens cost ₹75, how much do 8 pens cost? (a) ₹78 (b) ₹120 (c) ₹135 (d) ₹600
19. 19.₹286 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹22 (b) ₹88 (c) ₹198 (d) ₹143
20. 20.If 8 kites cost ₹168, how much do 9 kites cost? (a) ₹189 (b) ₹1512 (c) ₹169 (d) ₹210
21. 21.₹95 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹38 (b) ₹19 (c) ₹57 (d) ₹76
22. 22.₹238 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹136 (b) ₹119 (c) ₹102 (d) ₹34
23. 23.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 6 days
24. 24.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 39 days (c) 17 days (d) 40 days
25. 25.If 9 kites cost ₹99, how much do 4 kites cost? (a) ₹55 (b) ₹94 (c) ₹44 (d) ₹396
26. 26.₹114 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹19 (b) ₹114 (c) ₹95 (d) ₹57
27. 27.₹270 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹27 (b) ₹135 (c) ₹81 (d) ₹189
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) 6 days (d) 5 days
29. 29.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 2 days (d) 3 days
30. 30.₹441 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹441 (b) ₹392 (c) ₹49 (d) ₹393
31. 31.If 2 notebooks cost ₹10, how much do 7 notebooks cost? (a) ₹40 (b) ₹70 (c) ₹35 (d) ₹15
32. 32.₹60 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹30 (b) ₹40 (c) ₹20 (d) ₹60
33. 33.₹495 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹45 (b) ₹405 (c) ₹135 (d) ₹360
34. 34.₹396 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹44 (b) ₹198 (c) ₹308 (d) ₹88
35. 35.If 5 notebooks cost ₹80, how much do 7 notebooks cost? (a) ₹112 (b) ₹128 (c) ₹560 (d) ₹82
36. 36.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 15 days (d) 16 days
37. 37.₹396 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹288 (b) ₹36 (c) ₹198 (d) ₹108
38. 38.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 53 days (c) 52 days (d) 7 days
39. 39.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 10 days (d) 17 days
40. 40.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 29 days (b) 8 days (c) 16 days (d) 28 days

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