Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 945 · 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. 1.9 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) 28 days (d) 15 days
2. 2.If 7 mangoes cost ₹91, how much do 2 mangoes cost? (a) ₹182 (b) ₹86 (c) ₹26 (d) ₹39
3. 3.₹351 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹108 (b) ₹270 (c) ₹243 (d) ₹27
4. 4.₹195 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹150 (b) ₹60 (c) ₹135 (d) ₹15
5. 5.₹200 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹125 (b) ₹75 (c) ₹25 (d) ₹100
6. 6.₹296 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹296 (b) ₹259 (c) ₹37 (d) ₹148
7. 7.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 3 days (c) 2 days (d) 4 days
8. 8.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 9 days
9. 9.If 2 mangoes cost ₹8, how much do 12 mangoes cost? (a) ₹52 (b) ₹96 (c) ₹18 (d) ₹48
10. 10.If 3 notebooks cost ₹69, how much do 7 notebooks cost? (a) ₹483 (b) ₹73 (c) ₹161 (d) ₹184
11. 11.If 6 pens cost ₹66, how much do 7 pens cost? (a) ₹88 (b) ₹67 (c) ₹462 (d) ₹77
12. 12.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 22 days (c) 13 days (d) 21 days
13. 13.If 3 mangoes cost ₹60, how much do 6 mangoes cost? (a) ₹63 (b) ₹140 (c) ₹120 (d) ₹360
14. 14.If 3 notebooks cost ₹42, how much do 10 notebooks cost? (a) ₹420 (b) ₹49 (c) ₹140 (d) ₹154
15. 15.If 2 pens cost ₹48, how much do 12 pens cost? (a) ₹312 (b) ₹58 (c) ₹576 (d) ₹288
16. 16.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 21 days (c) 11 days (d) 22 days
17. 17.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 14 days (c) 9 days (d) 15 days
18. 18.₹290 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹203 (b) ₹145 (c) ₹29 (d) ₹87
19. 19.If 6 pens cost ₹36, how much do 9 pens cost? (a) ₹324 (b) ₹39 (c) ₹60 (d) ₹54
20. 20.If 7 pens cost ₹91, how much do 11 pens cost? (a) ₹95 (b) ₹156 (c) ₹1001 (d) ₹143
21. 21.₹98 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹14 (b) ₹84 (c) ₹49 (d) ₹98
22. 22.If 6 kites cost ₹138, how much do 7 kites cost? (a) ₹161 (b) ₹184 (c) ₹966 (d) ₹139
23. 23.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 5 days (d) 15 days
24. 24.If 6 pens cost ₹60, how much do 10 pens cost? (a) ₹110 (b) ₹100 (c) ₹600 (d) ₹64
25. 25.If 9 notebooks cost ₹144, how much do 3 notebooks cost? (a) ₹432 (b) ₹48 (c) ₹64 (d) ₹138
26. 26.If 9 pens cost ₹117, how much do 2 pens cost? (a) ₹26 (b) ₹110 (c) ₹39 (d) ₹234
27. 27.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 3 days (d) 5 days
28. 28.If 3 notebooks cost ₹27, how much do 9 notebooks cost? (a) ₹90 (b) ₹81 (c) ₹243 (d) ₹33
29. 29.If 3 notebooks cost ₹42, how much do 4 notebooks cost? (a) ₹56 (b) ₹70 (c) ₹168 (d) ₹43
30. 30.If 9 pens cost ₹225, how much do 12 pens cost? (a) ₹2700 (b) ₹228 (c) ₹325 (d) ₹300
31. 31.₹105 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹90 (b) ₹75 (c) ₹30 (d) ₹15
32. 32.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 10 days (d) 19 days
33. 33.If 7 mangoes cost ₹161, how much do 3 mangoes cost? (a) ₹69 (b) ₹92 (c) ₹483 (d) ₹157
34. 34.₹81 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹72 (b) ₹81 (c) ₹73 (d) ₹9
35. 35.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 9 days (d) 2 days
36. 36.₹150 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹30 (b) ₹90 (c) ₹60 (d) ₹75
37. 37.If 4 kites cost ₹92, how much do 2 kites cost? (a) ₹184 (b) ₹90 (c) ₹69 (d) ₹46
38. 38.₹144 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹72 (b) ₹12 (c) ₹84 (d) ₹60
39. 39.₹56 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹28 (b) ₹35 (c) ₹21 (d) ₹7
40. 40.₹217 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹31 (b) ₹186 (c) ₹217 (d) ₹187

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