Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 726 · 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 8 pens cost ₹88, how much do 3 pens cost? (a) ₹83 (b) ₹264 (c) ₹44 (d) ₹33
2. 2.If 3 notebooks cost ₹39, how much do 2 notebooks cost? (a) ₹26 (b) ₹39 (c) ₹78 (d) ₹38
3. 3.If 6 mangoes cost ₹102, how much do 9 mangoes cost? (a) ₹105 (b) ₹170 (c) ₹153 (d) ₹918
4. 4.₹390 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹273 (b) ₹39 (c) ₹117 (d) ₹195
5. 5.If 8 kites cost ₹120, how much do 3 kites cost? (a) ₹60 (b) ₹360 (c) ₹45 (d) ₹115
6. 6.If 4 kites cost ₹44, how much do 9 kites cost? (a) ₹49 (b) ₹99 (c) ₹396 (d) ₹110
7. 7.If 6 mangoes cost ₹42, how much do 9 mangoes cost? (a) ₹378 (b) ₹45 (c) ₹70 (d) ₹63
8. 8.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 16 days (b) 3 days (c) 13 days (d) 4 days
9. 9.If 9 notebooks cost ₹189, how much do 10 notebooks cost? (a) ₹1890 (b) ₹210 (c) ₹190 (d) ₹231
10. 10.₹77 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹55 (b) ₹44 (c) ₹33 (d) ₹11
11. 11.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 20 days (c) 12 days (d) 8 days
12. 12.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 14 days (d) 9 days
13. 13.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹108 (b) ₹12 (c) ₹84 (d) ₹60
14. 14.If 5 pens cost ₹15, how much do 4 pens cost? (a) ₹14 (b) ₹15 (c) ₹12 (d) ₹60
15. 15.If 9 pens cost ₹135, how much do 12 pens cost? (a) ₹195 (b) ₹1620 (c) ₹138 (d) ₹180
16. 16.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 13 days (d) 26 days
17. 17.If 6 pens cost ₹42, how much do 10 pens cost? (a) ₹77 (b) ₹420 (c) ₹46 (d) ₹70
18. 18.₹217 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹155 (b) ₹31 (c) ₹124 (d) ₹93
19. 19.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 7 days (d) 3 days
20. 20.₹242 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹66 (b) ₹121 (c) ₹176 (d) ₹22
21. 21.If 3 pens cost ₹9, how much do 5 pens cost? (a) ₹11 (b) ₹18 (c) ₹15 (d) ₹45
22. 22.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 20 days (c) 6 days (d) 15 days
23. 23.₹333 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹74 (b) ₹37 (c) ₹259 (d) ₹296
24. 24.₹136 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹17 (b) ₹136 (c) ₹119 (d) ₹68
25. 25.₹48 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹48 (b) ₹12 (c) ₹36 (d) ₹24
26. 26.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 2 days (d) 3 days
27. 27.If 2 pens cost ₹50, how much do 6 pens cost? (a) ₹300 (b) ₹150 (c) ₹175 (d) ₹54
28. 28.If 2 pens cost ₹20, how much do 3 pens cost? (a) ₹40 (b) ₹60 (c) ₹21 (d) ₹30
29. 29.If 3 pens cost ₹75, how much do 7 pens cost? (a) ₹525 (b) ₹79 (c) ₹200 (d) ₹175
30. 30.₹650 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹200 (b) ₹450 (c) ₹325 (d) ₹50
31. 31.₹90 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹90 (b) ₹80 (c) ₹45 (d) ₹10
32. 32.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 12 days (c) 19 days (d) 18 days
33. 33.9 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 19 days (b) 18 days (c) 3 days (d) 13 days
34. 34.₹100 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹50 (b) ₹100 (c) ₹10 (d) ₹90
35. 35.If 5 notebooks cost ₹90, how much do 8 notebooks cost? (a) ₹162 (b) ₹144 (c) ₹720 (d) ₹93
36. 36.₹225 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹25 (b) ₹150 (c) ₹100 (d) ₹125
37. 37.If 5 notebooks cost ₹50, how much do 7 notebooks cost? (a) ₹80 (b) ₹52 (c) ₹350 (d) ₹70
38. 38.₹224 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹224 (b) ₹192 (c) ₹112 (d) ₹32
39. 39.If 5 notebooks cost ₹90, how much do 3 notebooks cost? (a) ₹72 (b) ₹270 (c) ₹88 (d) ₹54
40. 40.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 9 days (d) 3 days

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