Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 936 · 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 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 7 days (d) 2 days
2. 2.₹286 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹26 (b) ₹143 (c) ₹182 (d) ₹104
3. 3.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 8 days (c) 11 days (d) 9 days
4. 4.₹348 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹29 (b) ₹174 (c) ₹203 (d) ₹145
5. 5.If 7 notebooks cost ₹105, how much do 5 notebooks cost? (a) ₹75 (b) ₹103 (c) ₹90 (d) ₹525
6. 6.If 5 kites cost ₹40, how much do 8 kites cost? (a) ₹320 (b) ₹64 (c) ₹72 (d) ₹43
7. 7.₹152 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹19 (b) ₹57 (c) ₹76 (d) ₹95
8. 8.If 9 notebooks cost ₹225, how much do 11 notebooks cost? (a) ₹227 (b) ₹2475 (c) ₹275 (d) ₹300
9. 9.If 8 notebooks cost ₹64, how much do 2 notebooks cost? (a) ₹16 (b) ₹128 (c) ₹24 (d) ₹58
10. 10.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 14 days (d) 9 days
11. 11.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹5 (b) ₹45 (c) ₹40 (d) ₹25
12. 12.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 11 days (d) 3 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. 14.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 12 days (d) 10 days
15. 15.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 14 days (d) 9 days
16. 16.If 5 notebooks cost ₹20, how much do 8 notebooks cost? (a) ₹160 (b) ₹32 (c) ₹36 (d) ₹23
17. 17.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 25 days (d) 17 days
18. 18.₹135 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹105 (b) ₹120 (c) ₹30 (d) ₹15
19. 19.If 3 notebooks cost ₹69, how much do 6 notebooks cost? (a) ₹138 (b) ₹414 (c) ₹72 (d) ₹161
20. 20.₹35 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹31 (b) ₹30 (c) ₹35 (d) ₹5
21. 21.₹308 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹154 (b) ₹264 (c) ₹44 (d) ₹308
22. 22.₹184 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹184 (b) ₹138 (c) ₹92 (d) ₹46
23. 23.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 7 days (c) 15 days (d) 34 days
24. 24.₹143 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹11 (b) ₹44 (c) ₹99 (d) ₹110
25. 25.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 3 days (d) 16 days
26. 26.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 9 days (d) 5 days
27. 27.If 2 kites cost ₹42, how much do 8 kites cost? (a) ₹168 (b) ₹336 (c) ₹189 (d) ₹48
28. 28.If 3 mangoes cost ₹51, how much do 6 mangoes cost? (a) ₹54 (b) ₹306 (c) ₹119 (d) ₹102
29. 29.₹324 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹162 (b) ₹144 (c) ₹36 (d) ₹180
30. 30.If 8 mangoes cost ₹200, how much do 9 mangoes cost? (a) ₹250 (b) ₹1800 (c) ₹225 (d) ₹201
31. 31.If 4 notebooks cost ₹24, how much do 9 notebooks cost? (a) ₹60 (b) ₹54 (c) ₹29 (d) ₹216
32. 32.If 7 mangoes cost ₹70, how much do 12 mangoes cost? (a) ₹130 (b) ₹120 (c) ₹840 (d) ₹75
33. 33.₹147 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹21 (b) ₹63 (c) ₹105 (d) ₹84
34. 34.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 9 days (d) 11 days
35. 35.If 4 pens cost ₹40, how much do 10 pens cost? (a) ₹100 (b) ₹46 (c) ₹400 (d) ₹110
36. 36.₹220 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹20 (b) ₹110 (c) ₹120 (d) ₹100
37. 37.₹15 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹11 (b) ₹5 (c) ₹15 (d) ₹10
38. 38.₹540 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹315 (b) ₹225 (c) ₹45 (d) ₹270
39. 39.If 7 notebooks cost ₹140, how much do 8 notebooks cost? (a) ₹141 (b) ₹1120 (c) ₹160 (d) ₹180
40. 40.If 6 pens cost ₹24, how much do 10 pens cost? (a) ₹44 (b) ₹28 (c) ₹240 (d) ₹40

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