Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 630 · 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. 1.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 6 days (d) 12 days
2. 2.₹308 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹154 (b) ₹110 (c) ₹198 (d) ₹22
3. 3.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 28 days (c) 17 days (d) 27 days
4. 4.If 6 kites cost ₹144, how much do 5 kites cost? (a) ₹720 (b) ₹143 (c) ₹120 (d) ₹144
5. 5.₹180 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹180 (b) ₹160 (c) ₹20 (d) ₹90
6. 6.If 6 pens cost ₹66, how much do 2 pens cost? (a) ₹33 (b) ₹22 (c) ₹62 (d) ₹132
7. 7.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 34 days (c) 15 days (d) 7 days
8. 8.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 2 days (c) 14 days (d) 4 days
9. 9.If 8 kites cost ₹152, how much do 5 kites cost? (a) ₹95 (b) ₹760 (c) ₹149 (d) ₹114
10. 10.₹60 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹10 (b) ₹30 (c) ₹50 (d) ₹60
11. 11.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 16 days (d) 11 days
12. 12.If 9 kites cost ₹81, how much do 6 kites cost? (a) ₹78 (b) ₹54 (c) ₹486 (d) ₹63
13. 13.If 3 kites cost ₹24, how much do 11 kites cost? (a) ₹264 (b) ₹32 (c) ₹88 (d) ₹96
14. 14.₹369 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹328 (b) ₹287 (c) ₹41 (d) ₹82
15. 15.If 6 pens cost ₹72, how much do 11 pens cost? (a) ₹144 (b) ₹77 (c) ₹792 (d) ₹132
16. 16.₹60 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹60 (b) ₹20 (c) ₹30 (d) ₹40
17. 17.₹280 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹20 (b) ₹100 (c) ₹140 (d) ₹180
18. 18.If 2 mangoes cost ₹38, how much do 10 mangoes cost? (a) ₹209 (b) ₹190 (c) ₹46 (d) ₹380
19. 19.₹328 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹123 (b) ₹164 (c) ₹205 (d) ₹41
20. 20.If 9 mangoes cost ₹117, how much do 12 mangoes cost? (a) ₹169 (b) ₹1404 (c) ₹156 (d) ₹120
21. 21.If 9 kites cost ₹162, how much do 8 kites cost? (a) ₹161 (b) ₹1296 (c) ₹144 (d) ₹162
22. 22.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 17 days (c) 13 days (d) 30 days
23. 23.If 7 pens cost ₹56, how much do 9 pens cost? (a) ₹72 (b) ₹58 (c) ₹80 (d) ₹504
24. 24.If 8 mangoes cost ₹104, how much do 9 mangoes cost? (a) ₹130 (b) ₹936 (c) ₹117 (d) ₹105
25. 25.₹286 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹143 (b) ₹198 (c) ₹22 (d) ₹88
26. 26.₹520 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹360 (b) ₹260 (c) ₹160 (d) ₹40
27. 27.If 2 pens cost ₹30, how much do 6 pens cost? (a) ₹180 (b) ₹90 (c) ₹34 (d) ₹105
28. 28.₹390 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹195 (b) ₹30 (c) ₹270 (d) ₹120
29. 29.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 8 days (d) 9 days
30. 30.₹387 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹43 (b) ₹344 (c) ₹86 (d) ₹301
31. 31.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 6 days (c) 3 days (d) 4 days
32. 32.If 4 mangoes cost ₹76, how much do 6 mangoes cost? (a) ₹114 (b) ₹456 (c) ₹78 (d) ₹133
33. 33.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 13 days (d) 7 days
34. 34.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 2 days (c) 3 days (d) 4 days
35. 35.If 3 mangoes cost ₹27, how much do 9 mangoes cost? (a) ₹81 (b) ₹33 (c) ₹90 (d) ₹243
36. 36.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 8 days (d) 7 days
37. 37.If 5 pens cost ₹15, how much do 7 pens cost? (a) ₹17 (b) ₹21 (c) ₹24 (d) ₹105
38. 38.If 5 notebooks cost ₹110, how much do 8 notebooks cost? (a) ₹113 (b) ₹880 (c) ₹198 (d) ₹176
39. 39.If 3 mangoes cost ₹54, how much do 5 mangoes cost? (a) ₹270 (b) ₹56 (c) ₹108 (d) ₹90
40. 40.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 42 days (d) 43 days

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