Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 989 · 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. 1.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 8 days (c) 7 days (d) 6 days
2. 2.If 4 pens cost ₹40, how much do 2 pens cost? (a) ₹20 (b) ₹30 (c) ₹80 (d) ₹38
3. 3.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 19 days (d) 2 days
4. 4.If 2 mangoes cost ₹42, how much do 9 mangoes cost? (a) ₹210 (b) ₹189 (c) ₹49 (d) ₹378
5. 5.If 3 kites cost ₹66, how much do 4 kites cost? (a) ₹110 (b) ₹67 (c) ₹264 (d) ₹88
6. 6.₹442 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹306 (b) ₹34 (c) ₹136 (d) ₹221
7. 7.₹172 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹43 (b) ₹172 (c) ₹129 (d) ₹86
8. 8.If 6 pens cost ₹114, how much do 12 pens cost? (a) ₹120 (b) ₹247 (c) ₹228 (d) ₹1368
9. 9.If 4 pens cost ₹20, how much do 10 pens cost? (a) ₹50 (b) ₹55 (c) ₹200 (d) ₹26
10. 10.If 6 kites cost ₹84, how much do 5 kites cost? (a) ₹83 (b) ₹420 (c) ₹70 (d) ₹84
11. 11.₹162 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹27 (b) ₹135 (c) ₹81 (d) ₹162
12. 12.₹484 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹44 (b) ₹242 (c) ₹176 (d) ₹308
13. 13.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 7 days (c) 39 days (d) 19 days
14. 14.₹77 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹56 (b) ₹21 (c) ₹7 (d) ₹63
15. 15.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 17 days (d) 4 days
16. 16.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 12 days (d) 2 days
17. 17.If 5 kites cost ₹60, how much do 3 kites cost? (a) ₹180 (b) ₹48 (c) ₹36 (d) ₹58
18. 18.If 8 notebooks cost ₹176, how much do 7 notebooks cost? (a) ₹1232 (b) ₹175 (c) ₹176 (d) ₹154
19. 19.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 3 days (d) 2 days
20. 20.₹329 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹235 (b) ₹141 (c) ₹47 (d) ₹188
21. 21.₹112 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹96 (b) ₹112 (c) ₹16 (d) ₹56
22. 22.If 5 pens cost ₹65, how much do 10 pens cost? (a) ₹70 (b) ₹650 (c) ₹143 (d) ₹130
23. 23.If 6 pens cost ₹84, how much do 2 pens cost? (a) ₹42 (b) ₹168 (c) ₹28 (d) ₹80
24. 24.₹129 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹86 (b) ₹87 (c) ₹43 (d) ₹129
25. 25.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 8 days (d) 7 days
26. 26.₹286 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹104 (b) ₹182 (c) ₹26 (d) ₹143
27. 27.₹63 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹56 (b) ₹14 (c) ₹49 (d) ₹7
28. 28.₹54 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹54 (b) ₹48 (c) ₹27 (d) ₹6
29. 29.If 2 mangoes cost ₹8, how much do 4 mangoes cost? (a) ₹10 (b) ₹32 (c) ₹16 (d) ₹20
30. 30.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 1 day (c) 29 days (d) 13 days
31. 31.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 42 days (d) 43 days
32. 32.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 2 days (d) 12 days
33. 33.If 6 notebooks cost ₹30, how much do 2 notebooks cost? (a) ₹10 (b) ₹15 (c) ₹26 (d) ₹60
34. 34.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹16 (b) ₹64 (c) ₹72 (d) ₹80
35. 35.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 15 days (c) 8 days (d) 14 days
36. 36.If 4 pens cost ₹92, how much do 7 pens cost? (a) ₹644 (b) ₹161 (c) ₹184 (d) ₹95
37. 37.₹400 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹150 (b) ₹200 (c) ₹250 (d) ₹50
38. 38.If 3 mangoes cost ₹45, how much do 5 mangoes cost? (a) ₹75 (b) ₹90 (c) ₹225 (d) ₹47
39. 39.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 13 days (b) 2 days (c) 3 days (d) 4 days
40. 40.₹144 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹144 (b) ₹72 (c) ₹128 (d) ₹16

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