Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 833 · 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. 1.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 7 days (d) 6 days
2. 2.If 7 mangoes cost ₹77, how much do 6 mangoes cost? (a) ₹462 (b) ₹77 (c) ₹76 (d) ₹66
3. 3.₹105 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹75 (b) ₹15 (c) ₹45 (d) ₹60
4. 4.₹324 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹36 (b) ₹252 (c) ₹162 (d) ₹72
5. 5.₹225 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹201 (b) ₹25 (c) ₹225 (d) ₹200
6. 6.₹252 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹36 (b) ₹144 (c) ₹108 (d) ₹126
7. 7.If 2 pens cost ₹12, how much do 6 pens cost? (a) ₹42 (b) ₹72 (c) ₹36 (d) ₹16
8. 8.₹182 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹112 (b) ₹91 (c) ₹70 (d) ₹14
9. 9.₹315 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹45 (b) ₹270 (c) ₹315 (d) ₹271
10. 10.If 3 kites cost ₹21, how much do 2 kites cost? (a) ₹42 (b) ₹14 (c) ₹21 (d) ₹20
11. 11.₹205 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹205 (b) ₹165 (c) ₹41 (d) ₹164
12. 12.₹351 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹135 (b) ₹243 (c) ₹27 (d) ₹216
13. 13.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 17 days (c) 4 days (d) 16 days
14. 14.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 3 days
15. 15.₹182 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹91 (b) ₹26 (c) ₹104 (d) ₹78
16. 16.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹11 (b) ₹44 (c) ₹66 (d) ₹55
17. 17.₹418 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹152 (b) ₹266 (c) ₹38 (d) ₹209
18. 18.If 2 notebooks cost ₹20, how much do 3 notebooks cost? (a) ₹21 (b) ₹60 (c) ₹40 (d) ₹30
19. 19.If 8 kites cost ₹144, how much do 2 kites cost? (a) ₹288 (b) ₹138 (c) ₹54 (d) ₹36
20. 20.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹78 (b) ₹65 (c) ₹91 (d) ₹13
21. 21.If 8 kites cost ₹120, how much do 3 kites cost? (a) ₹360 (b) ₹115 (c) ₹60 (d) ₹45
22. 22.If 9 pens cost ₹81, how much do 11 pens cost? (a) ₹891 (b) ₹83 (c) ₹99 (d) ₹108
23. 23.If 4 kites cost ₹56, how much do 3 kites cost? (a) ₹55 (b) ₹56 (c) ₹42 (d) ₹168
24. 24.If 2 kites cost ₹16, how much do 7 kites cost? (a) ₹21 (b) ₹64 (c) ₹112 (d) ₹56
25. 25.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 13 days (d) 15 days
26. 26.₹363 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹264 (b) ₹33 (c) ₹297 (d) ₹99
27. 27.₹132 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹12 (b) ₹66 (c) ₹96 (d) ₹36
28. 28.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 16 days (d) 10 days
29. 29.If 2 notebooks cost ₹12, how much do 4 notebooks cost? (a) ₹24 (b) ₹30 (c) ₹14 (d) ₹48
30. 30.₹184 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹46 (b) ₹92 (c) ₹138 (d) ₹184
31. 31.If 9 notebooks cost ₹36, how much do 2 notebooks cost? (a) ₹12 (b) ₹29 (c) ₹72 (d) ₹8
32. 32.₹484 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹132 (b) ₹242 (c) ₹44 (d) ₹352
33. 33.If 7 pens cost ₹77, how much do 8 pens cost? (a) ₹88 (b) ₹78 (c) ₹99 (d) ₹616
34. 34.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 10 days (d) 1 day
35. 35.₹120 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹60 (b) ₹80 (c) ₹40 (d) ₹120
36. 36.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 16 days (c) 26 days (d) 10 days
37. 37.5 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) 5 days (d) 6 days
38. 38.If 6 pens cost ₹48, how much do 7 pens cost? (a) ₹64 (b) ₹49 (c) ₹56 (d) ₹336
39. 39.If 8 kites cost ₹24, how much do 12 kites cost? (a) ₹39 (b) ₹36 (c) ₹288 (d) ₹28
40. 40.If 7 notebooks cost ₹35, how much do 4 notebooks cost? (a) ₹20 (b) ₹140 (c) ₹32 (d) ₹25

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