Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 25 · 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 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 22 days (c) 21 days (d) 13 days
2. 2.If 3 pens cost ₹72, how much do 4 pens cost? (a) ₹96 (b) ₹73 (c) ₹120 (d) ₹288
3. 3.₹296 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹148 (b) ₹37 (c) ₹111 (d) ₹185
4. 4.If 7 pens cost ₹28, how much do 4 pens cost? (a) ₹112 (b) ₹16 (c) ₹25 (d) ₹20
5. 5.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 14 days (d) 15 days
6. 6.₹490 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹343 (b) ₹49 (c) ₹147 (d) ₹245
7. 7.₹64 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹64 (b) ₹16 (c) ₹48 (d) ₹32
8. 8.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹13 (b) ₹91 (c) ₹65 (d) ₹78
9. 9.If 8 pens cost ₹160, how much do 12 pens cost? (a) ₹164 (b) ₹1920 (c) ₹260 (d) ₹240
10. 10.₹429 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹195 (b) ₹39 (c) ₹234 (d) ₹273
11. 11.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹72 (b) ₹81 (c) ₹9 (d) ₹45
12. 12.If 4 notebooks cost ₹96, how much do 11 notebooks cost? (a) ₹1056 (b) ₹103 (c) ₹264 (d) ₹288
13. 13.₹253 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹184 (b) ₹23 (c) ₹92 (d) ₹161
14. 14.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 7 days (d) 4 days
15. 15.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 5 days (c) 6 days (d) 4 days
16. 16.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 3 days (d) 6 days
17. 17.If 7 kites cost ₹154, how much do 12 kites cost? (a) ₹159 (b) ₹286 (c) ₹264 (d) ₹1848
18. 18.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 21 days (c) 11 days (d) 22 days
19. 19.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 28 days (b) 10 days (c) 18 days (d) 7 days
20. 20.If 3 pens cost ₹51, how much do 4 pens cost? (a) ₹85 (b) ₹204 (c) ₹52 (d) ₹68
21. 21.₹360 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹150 (b) ₹210 (c) ₹30 (d) ₹180
22. 22.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 27 days (b) 1 day (c) 17 days (d) 3 days
23. 23.₹156 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹130 (b) ₹78 (c) ₹26 (d) ₹156
24. 24.₹105 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹15 (b) ₹60 (c) ₹45 (d) ₹75
25. 25.₹75 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹50 (b) ₹51 (c) ₹75 (d) ₹25
26. 26.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 9 days (d) 13 days
27. 27.If 4 notebooks cost ₹72, how much do 5 notebooks cost? (a) ₹73 (b) ₹360 (c) ₹108 (d) ₹90
28. 28.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 5 days
29. 29.₹70 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹50 (b) ₹20 (c) ₹35 (d) ₹10
30. 30.If 6 notebooks cost ₹150, how much do 7 notebooks cost? (a) ₹200 (b) ₹175 (c) ₹1050 (d) ₹151
31. 31.If 5 mangoes cost ₹110, how much do 6 mangoes cost? (a) ₹111 (b) ₹154 (c) ₹660 (d) ₹132
32. 32.₹384 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹32 (b) ₹224 (c) ₹192 (d) ₹160
33. 33.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 3 days (c) 4 days (d) 2 days
34. 34.If 7 pens cost ₹161, how much do 8 pens cost? (a) ₹162 (b) ₹1288 (c) ₹184 (d) ₹207
35. 35.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 15 days (d) 27 days
36. 36.₹168 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹21 (b) ₹168 (c) ₹84 (d) ₹147
37. 37.If 4 pens cost ₹76, how much do 2 pens cost? (a) ₹38 (b) ₹74 (c) ₹152 (d) ₹57
38. 38.If 3 mangoes cost ₹66, how much do 9 mangoes cost? (a) ₹72 (b) ₹220 (c) ₹594 (d) ₹198
39. 39.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹35 (b) ₹7 (c) ₹63 (d) ₹56
40. 40.₹369 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹164 (b) ₹41 (c) ₹246 (d) ₹205

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