Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 453 · 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 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 13 days (c) 5 days (d) 4 days
2. 2.₹240 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹120 (b) ₹168 (c) ₹24 (d) ₹72
3. 3.₹195 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹135 (b) ₹120 (c) ₹15 (d) ₹75
4. 4.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹15 (b) ₹105 (c) ₹90 (d) ₹75
5. 5.If 8 kites cost ₹160, how much do 7 kites cost? (a) ₹159 (b) ₹1120 (c) ₹140 (d) ₹160
6. 6.If 9 notebooks cost ₹81, how much do 3 notebooks cost? (a) ₹36 (b) ₹75 (c) ₹243 (d) ₹27
7. 7.If 6 kites cost ₹120, how much do 11 kites cost? (a) ₹125 (b) ₹220 (c) ₹240 (d) ₹1320
8. 8.₹135 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹15 (b) ₹30 (c) ₹120 (d) ₹105
9. 9.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 14 days (c) 16 days (d) 9 days
10. 10.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 16 days (d) 5 days
11. 11.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 17 days (d) 25 days
12. 12.₹273 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹235 (b) ₹273 (c) ₹39 (d) ₹234
13. 13.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 32 days (d) 33 days
14. 14.₹98 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹14 (b) ₹49 (c) ₹70 (d) ₹28
15. 15.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 2 days (c) 3 days (d) 4 days
16. 16.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 28 days (c) 16 days (d) 7 days
17. 17.If 8 mangoes cost ₹128, how much do 9 mangoes cost? (a) ₹1152 (b) ₹160 (c) ₹144 (d) ₹129
18. 18.If 2 pens cost ₹40, how much do 7 pens cost? (a) ₹45 (b) ₹160 (c) ₹280 (d) ₹140
19. 19.If 5 kites cost ₹25, how much do 11 kites cost? (a) ₹60 (b) ₹31 (c) ₹55 (d) ₹275
20. 20.₹144 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹112 (b) ₹32 (c) ₹16 (d) ₹72
21. 21.₹200 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹120 (b) ₹100 (c) ₹40 (d) ₹80
22. 22.If 8 mangoes cost ₹24, how much do 3 mangoes cost? (a) ₹72 (b) ₹19 (c) ₹12 (d) ₹9
23. 23.If 8 pens cost ₹48, how much do 5 pens cost? (a) ₹36 (b) ₹45 (c) ₹30 (d) ₹240
24. 24.If 4 pens cost ₹28, how much do 7 pens cost? (a) ₹196 (b) ₹49 (c) ₹56 (d) ₹31
25. 25.If 2 notebooks cost ₹42, how much do 3 notebooks cost? (a) ₹126 (b) ₹84 (c) ₹63 (d) ₹43
26. 26.If 6 notebooks cost ₹102, how much do 2 notebooks cost? (a) ₹98 (b) ₹34 (c) ₹51 (d) ₹204
27. 27.₹242 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹22 (b) ₹121 (c) ₹198 (d) ₹44
28. 28.If 3 pens cost ₹45, how much do 12 pens cost? (a) ₹195 (b) ₹540 (c) ₹180 (d) ₹54
29. 29.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 35 days (d) 36 days
30. 30.If 3 pens cost ₹12, how much do 10 pens cost? (a) ₹40 (b) ₹44 (c) ₹120 (d) ₹19
31. 31.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 31 days (c) 30 days (d) 6 days
32. 32.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 15 days (d) 27 days
33. 33.₹99 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹54 (b) ₹63 (c) ₹9 (d) ₹45
34. 34.If 5 pens cost ₹90, how much do 10 pens cost? (a) ₹180 (b) ₹900 (c) ₹95 (d) ₹198
35. 35.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 3 days
36. 36.₹30 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹10 (b) ₹15 (c) ₹20 (d) ₹30
37. 37.If 5 notebooks cost ₹90, how much do 11 notebooks cost? (a) ₹216 (b) ₹990 (c) ₹96 (d) ₹198
38. 38.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 11 days (d) 15 days
39. 39.₹203 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹29 (b) ₹203 (c) ₹175 (d) ₹174
40. 40.If 3 pens cost ₹63, how much do 6 pens cost? (a) ₹378 (b) ₹126 (c) ₹147 (d) ₹66

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