Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 274 · 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 6 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 7 days
2. 2.₹390 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹39 (b) ₹390 (c) ₹195 (d) ₹351
3. 3.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 25 days (c) 7 days (d) 13 days
4. 4.₹189 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹147 (b) ₹42 (c) ₹21 (d) ₹168
5. 5.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 15 days (d) 28 days
6. 6.If 7 pens cost ₹42, how much do 9 pens cost? (a) ₹60 (b) ₹54 (c) ₹44 (d) ₹378
7. 7.If 5 pens cost ₹40, how much do 3 pens cost? (a) ₹32 (b) ₹38 (c) ₹24 (d) ₹120
8. 8.If 9 kites cost ₹54, how much do 7 kites cost? (a) ₹52 (b) ₹48 (c) ₹42 (d) ₹378
9. 9.If 9 notebooks cost ₹171, how much do 3 notebooks cost? (a) ₹76 (b) ₹513 (c) ₹165 (d) ₹57
10. 10.If 7 pens cost ₹147, how much do 6 pens cost? (a) ₹126 (b) ₹146 (c) ₹147 (d) ₹882
11. 11.₹96 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹48 (b) ₹96 (c) ₹32 (d) ₹64
12. 12.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 7 days (d) 20 days
13. 13.₹224 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹16 (b) ₹112 (c) ₹80 (d) ₹144
14. 14.₹390 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹195 (b) ₹240 (c) ₹30 (d) ₹150
15. 15.If 7 mangoes cost ₹84, how much do 3 mangoes cost? (a) ₹252 (b) ₹48 (c) ₹36 (d) ₹80
16. 16.If 2 kites cost ₹16, how much do 3 kites cost? (a) ₹17 (b) ₹32 (c) ₹48 (d) ₹24
17. 17.If 2 notebooks cost ₹44, how much do 5 notebooks cost? (a) ₹47 (b) ₹110 (c) ₹220 (d) ₹132
18. 18.If 5 notebooks cost ₹60, how much do 11 notebooks cost? (a) ₹66 (b) ₹144 (c) ₹660 (d) ₹132
19. 19.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 11 days
20. 20.If 9 pens cost ₹45, how much do 8 pens cost? (a) ₹44 (b) ₹40 (c) ₹45 (d) ₹360
21. 21.If 3 pens cost ₹30, how much do 4 pens cost? (a) ₹120 (b) ₹31 (c) ₹50 (d) ₹40
22. 22.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 17 days (d) 6 days
23. 23.If 7 pens cost ₹91, how much do 12 pens cost? (a) ₹96 (b) ₹169 (c) ₹156 (d) ₹1092
24. 24.If 4 mangoes cost ₹28, how much do 2 mangoes cost? (a) ₹26 (b) ₹56 (c) ₹21 (d) ₹14
25. 25.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 1 day
26. 26.₹315 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹245 (b) ₹280 (c) ₹70 (d) ₹35
27. 27.₹21 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹21 (b) ₹14 (c) ₹7 (d) ₹15
28. 28.₹150 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹75 (b) ₹150 (c) ₹30 (d) ₹120
29. 29.₹141 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹141 (b) ₹94 (c) ₹47 (d) ₹95
30. 30.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 57 days (c) 20 days (d) 56 days
31. 31.₹105 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹15 (b) ₹30 (c) ₹90 (d) ₹75
32. 32.₹45 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹37 (b) ₹45 (c) ₹9 (d) ₹36
33. 33.If 2 pens cost ₹22, how much do 7 pens cost? (a) ₹27 (b) ₹154 (c) ₹77 (d) ₹88
34. 34.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 26 days (d) 11 days
35. 35.If 5 pens cost ₹120, how much do 4 pens cost? (a) ₹480 (b) ₹119 (c) ₹96 (d) ₹120
36. 36.If 4 pens cost ₹48, how much do 3 pens cost? (a) ₹47 (b) ₹48 (c) ₹144 (d) ₹36
37. 37.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 9 days (d) 7 days
38. 38.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 12 days (d) 7 days
39. 39.₹429 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹39 (b) ₹351 (c) ₹390 (d) ₹78
40. 40.If 9 mangoes cost ₹162, how much do 4 mangoes cost? (a) ₹157 (b) ₹648 (c) ₹90 (d) ₹72

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