Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 683 · 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 4 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 6 days (d) 4 days
2. 2.5 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 13 days (d) 9 days
3. 3.If 8 pens cost ₹40, how much do 6 pens cost? (a) ₹30 (b) ₹240 (c) ₹35 (d) ₹38
4. 4.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 34 days (c) 33 days (d) 7 days
5. 5.₹480 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹40 (b) ₹240 (c) ₹200 (d) ₹280
6. 6.3 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) 4 days (d) 2 days
7. 7.If 7 kites cost ₹168, how much do 2 kites cost? (a) ₹336 (b) ₹72 (c) ₹48 (d) ₹163
8. 8.If 5 notebooks cost ₹50, how much do 6 notebooks cost? (a) ₹51 (b) ₹70 (c) ₹300 (d) ₹60
9. 9.₹348 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹203 (b) ₹145 (c) ₹174 (d) ₹29
10. 10.If 2 pens cost ₹48, how much do 5 pens cost? (a) ₹240 (b) ₹51 (c) ₹144 (d) ₹120
11. 11.₹198 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹99 (b) ₹22 (c) ₹88 (d) ₹110
12. 12.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 20 days (d) 16 days
13. 13.₹112 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹56 (b) ₹42 (c) ₹14 (d) ₹70
14. 14.₹88 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹88 (b) ₹11 (c) ₹77 (d) ₹44
15. 15.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 17 days (d) 5 days
16. 16.If 4 kites cost ₹36, how much do 9 kites cost? (a) ₹81 (b) ₹41 (c) ₹324 (d) ₹90
17. 17.₹242 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹121 (b) ₹132 (c) ₹110 (d) ₹22
18. 18.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 30 days (d) 31 days
19. 19.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 40 days (c) 39 days (d) 7 days
20. 20.₹110 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹22 (b) ₹44 (c) ₹66 (d) ₹55
21. 21.If 5 notebooks cost ₹120, how much do 3 notebooks cost? (a) ₹96 (b) ₹118 (c) ₹360 (d) ₹72
22. 22.₹243 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹27 (b) ₹162 (c) ₹108 (d) ₹135
23. 23.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 16 days (d) 6 days
24. 24.₹400 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹200 (b) ₹360 (c) ₹400 (d) ₹40
25. 25.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 3 days
26. 26.7 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 15 days (d) 14 days
27. 27.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 15 days (c) 14 days (d) 10 days
28. 28.If 7 notebooks cost ₹84, how much do 2 notebooks cost? (a) ₹168 (b) ₹79 (c) ₹24 (d) ₹36
29. 29.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 17 days (d) 25 days
30. 30.If 2 pens cost ₹26, how much do 6 pens cost? (a) ₹30 (b) ₹91 (c) ₹156 (d) ₹78
31. 31.₹95 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹38 (b) ₹19 (c) ₹57 (d) ₹76
32. 32.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 20 days (b) 7 days (c) 5 days (d) 13 days
33. 33.If 9 mangoes cost ₹54, how much do 2 mangoes cost? (a) ₹18 (b) ₹12 (c) ₹108 (d) ₹47
34. 34.₹30 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹15 (b) ₹6 (c) ₹30 (d) ₹24
35. 35.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹5 (b) ₹15 (c) ₹20 (d) ₹10
36. 36.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 5 days (c) 4 days (d) 3 days
37. 37.If 9 pens cost ₹99, how much do 4 pens cost? (a) ₹55 (b) ₹396 (c) ₹94 (d) ₹44
38. 38.If 8 pens cost ₹56, how much do 2 pens cost? (a) ₹112 (b) ₹50 (c) ₹14 (d) ₹21
39. 39.If 3 pens cost ₹12, how much do 12 pens cost? (a) ₹144 (b) ₹52 (c) ₹21 (d) ₹48
40. 40.If 3 kites cost ₹51, how much do 7 kites cost? (a) ₹55 (b) ₹357 (c) ₹119 (d) ₹136

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