Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 731 · 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. 1.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 10 days (d) 4 days
2. 2.If 3 notebooks cost ₹33, how much do 4 notebooks cost? (a) ₹55 (b) ₹44 (c) ₹34 (d) ₹132
3. 3.If 5 pens cost ₹60, how much do 12 pens cost? (a) ₹156 (b) ₹720 (c) ₹144 (d) ₹67
4. 4.If 6 kites cost ₹138, how much do 8 kites cost? (a) ₹1104 (b) ₹140 (c) ₹207 (d) ₹184
5. 5.₹84 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹24 (b) ₹42 (c) ₹60 (d) ₹12
6. 6.₹112 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹32 (b) ₹80 (c) ₹56 (d) ₹16
7. 7.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 11 days (d) 8 days
8. 8.If 5 pens cost ₹95, how much do 9 pens cost? (a) ₹99 (b) ₹190 (c) ₹855 (d) ₹171
9. 9.If 6 pens cost ₹18, how much do 7 pens cost? (a) ₹126 (b) ₹21 (c) ₹24 (d) ₹19
10. 10.₹132 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹12 (b) ₹84 (c) ₹66 (d) ₹48
11. 11.₹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
12. 12.3 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) 3 days (d) 2 days
13. 13.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 15 days (d) 3 days
14. 14.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 27 days (d) 26 days
15. 15.If 3 mangoes cost ₹66, how much do 12 mangoes cost? (a) ₹286 (b) ₹264 (c) ₹792 (d) ₹75
16. 16.₹473 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹43 (b) ₹344 (c) ₹172 (d) ₹301
17. 17.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 18 days (d) 8 days
18. 18.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 18 days (c) 4 days (d) 5 days
19. 19.If 7 kites cost ₹147, how much do 6 kites cost? (a) ₹147 (b) ₹882 (c) ₹126 (d) ₹146
20. 20.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 23 days (c) 9 days (d) 22 days
21. 21.₹84 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹42 (b) ₹14 (c) ₹84 (d) ₹70
22. 22.If 2 notebooks cost ₹42, how much do 7 notebooks cost? (a) ₹47 (b) ₹168 (c) ₹147 (d) ₹294
23. 23.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 13 days (d) 9 days
24. 24.₹160 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹80 (b) ₹160 (c) ₹128 (d) ₹32
25. 25.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 7 days (d) 25 days
26. 26.If 8 kites cost ₹104, how much do 2 kites cost? (a) ₹208 (b) ₹98 (c) ₹39 (d) ₹26
27. 27.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 19 days (d) 16 days
28. 28.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹40 (b) ₹25 (c) ₹45 (d) ₹5
29. 29.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹40 (b) ₹8 (c) ₹52 (d) ₹64
30. 30.If 2 kites cost ₹14, how much do 12 kites cost? (a) ₹24 (b) ₹84 (c) ₹91 (d) ₹168
31. 31.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 9 days (d) 8 days
32. 32.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 11 days
33. 33.₹156 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹12 (b) ₹96 (c) ₹78 (d) ₹60
34. 34.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 1 day (d) 17 days
35. 35.If 4 notebooks cost ₹100, how much do 9 notebooks cost? (a) ₹900 (b) ₹225 (c) ₹105 (d) ₹250
36. 36.If 9 pens cost ₹54, how much do 3 pens cost? (a) ₹162 (b) ₹24 (c) ₹48 (d) ₹18
37. 37.If 4 mangoes cost ₹20, how much do 7 mangoes cost? (a) ₹23 (b) ₹40 (c) ₹140 (d) ₹35
38. 38.₹150 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹150 (b) ₹75 (c) ₹125 (d) ₹25
39. 39.₹77 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹63 (b) ₹56 (c) ₹7 (d) ₹21
40. 40.₹98 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹56 (b) ₹49 (c) ₹42 (d) ₹14

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