Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 840 · 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.If 2 pens cost ₹20, how much do 4 pens cost? (a) ₹50 (b) ₹40 (c) ₹22 (d) ₹80
2. 2.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 10 days (d) 16 days
3. 3.If 6 notebooks cost ₹90, how much do 8 notebooks cost? (a) ₹135 (b) ₹92 (c) ₹720 (d) ₹120
4. 4.4 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
5. 5.If 9 notebooks cost ₹63, how much do 2 notebooks cost? (a) ₹21 (b) ₹14 (c) ₹126 (d) ₹56
6. 6.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 11 days (d) 14 days
7. 7.If 2 kites cost ₹12, how much do 3 kites cost? (a) ₹24 (b) ₹13 (c) ₹36 (d) ₹18
8. 8.₹95 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹95 (b) ₹77 (c) ₹76 (d) ₹19
9. 9.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 13 days (c) 3 days (d) 28 days
10. 10.If 9 notebooks cost ₹126, how much do 2 notebooks cost? (a) ₹252 (b) ₹42 (c) ₹28 (d) ₹119
11. 11.If 6 kites cost ₹150, how much do 2 kites cost? (a) ₹300 (b) ₹75 (c) ₹146 (d) ₹50
12. 12.If 3 pens cost ₹15, how much do 2 pens cost? (a) ₹15 (b) ₹30 (c) ₹10 (d) ₹14
13. 13.If 7 kites cost ₹133, how much do 6 kites cost? (a) ₹132 (b) ₹114 (c) ₹133 (d) ₹798
14. 14.If 3 pens cost ₹57, how much do 11 pens cost? (a) ₹65 (b) ₹627 (c) ₹209 (d) ₹228
15. 15.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 22 days (d) 21 days
16. 16.₹123 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹83 (b) ₹123 (c) ₹41 (d) ₹82
17. 17.If 6 mangoes cost ₹84, how much do 4 mangoes cost? (a) ₹336 (b) ₹70 (c) ₹82 (d) ₹56
18. 18.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 9 days (d) 16 days
19. 19.If 2 pens cost ₹26, how much do 12 pens cost? (a) ₹312 (b) ₹169 (c) ₹156 (d) ₹36
20. 20.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 17 days
21. 21.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹40 (b) ₹45 (c) ₹5 (d) ₹25
22. 22.If 8 pens cost ₹120, how much do 7 pens cost? (a) ₹105 (b) ₹840 (c) ₹120 (d) ₹119
23. 23.If 7 mangoes cost ₹70, how much do 11 mangoes cost? (a) ₹110 (b) ₹74 (c) ₹120 (d) ₹770
24. 24.If 4 kites cost ₹44, how much do 12 kites cost? (a) ₹143 (b) ₹52 (c) ₹132 (d) ₹528
25. 25.₹33 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹11 (b) ₹23 (c) ₹33 (d) ₹22
26. 26.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 2 days (c) 33 days (d) 32 days
27. 27.₹429 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹165 (b) ₹264 (c) ₹297 (d) ₹33
28. 28.If 8 mangoes cost ₹40, how much do 11 mangoes cost? (a) ₹440 (b) ₹43 (c) ₹60 (d) ₹55
29. 29.₹150 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹45 (b) ₹75 (c) ₹105 (d) ₹15
30. 30.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 7 days (d) 1 day
31. 31.₹116 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹29 (b) ₹87 (c) ₹116 (d) ₹58
32. 32.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 25 days (d) 13 days
33. 33.₹55 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹45 (b) ₹5 (c) ₹15 (d) ₹40
34. 34.₹507 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹351 (b) ₹39 (c) ₹312 (d) ₹195
35. 35.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 4 days (d) 27 days
36. 36.If 3 kites cost ₹39, how much do 6 kites cost? (a) ₹78 (b) ₹91 (c) ₹234 (d) ₹42
37. 37.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 20 days (d) 21 days
38. 38.If 7 notebooks cost ₹105, how much do 10 notebooks cost? (a) ₹165 (b) ₹150 (c) ₹108 (d) ₹1050
39. 39.₹506 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹276 (b) ₹230 (c) ₹253 (d) ₹46
40. 40.If 3 mangoes cost ₹15, how much do 4 mangoes cost? (a) ₹20 (b) ₹60 (c) ₹25 (d) ₹16

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