Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 707 · 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.₹69 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹47 (b) ₹23 (c) ₹69 (d) ₹46
2. 2.₹559 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹387 (b) ₹215 (c) ₹344 (d) ₹43
3. 3.₹341 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹217 (b) ₹31 (c) ₹248 (d) ₹124
4. 4.If 3 notebooks cost ₹57, how much do 7 notebooks cost? (a) ₹61 (b) ₹399 (c) ₹152 (d) ₹133
5. 5.If 4 kites cost ₹20, how much do 2 kites cost? (a) ₹15 (b) ₹40 (c) ₹10 (d) ₹18
6. 6.If 3 pens cost ₹30, how much do 5 pens cost? (a) ₹60 (b) ₹32 (c) ₹150 (d) ₹50
7. 7.If 7 pens cost ₹161, how much do 3 pens cost? (a) ₹483 (b) ₹69 (c) ₹157 (d) ₹92
8. 8.If 8 mangoes cost ₹64, how much do 3 mangoes cost? (a) ₹59 (b) ₹192 (c) ₹24 (d) ₹32
9. 9.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 54 days (b) 55 days (c) 5 days (d) 19 days
10. 10.₹99 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹90 (b) ₹9 (c) ₹81 (d) ₹18
11. 11.₹55 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹5 (b) ₹40 (c) ₹45 (d) ₹15
12. 12.6 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 16 days (d) 14 days
13. 13.₹98 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹7 (b) ₹63 (c) ₹35 (d) ₹49
14. 14.If 3 notebooks cost ₹39, how much do 4 notebooks cost? (a) ₹52 (b) ₹65 (c) ₹156 (d) ₹40
15. 15.₹296 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹111 (b) ₹148 (c) ₹185 (d) ₹37
16. 16.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹24 (b) ₹96 (c) ₹120 (d) ₹72
17. 17.If 5 notebooks cost ₹90, how much do 9 notebooks cost? (a) ₹810 (b) ₹162 (c) ₹94 (d) ₹180
18. 18.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 13 days (c) 8 days (d) 11 days
19. 19.If 8 pens cost ₹72, how much do 7 pens cost? (a) ₹71 (b) ₹63 (c) ₹72 (d) ₹504
20. 20.If 2 pens cost ₹50, how much do 12 pens cost? (a) ₹600 (b) ₹60 (c) ₹300 (d) ₹325
21. 21.If 5 mangoes cost ₹120, how much do 10 mangoes cost? (a) ₹240 (b) ₹1200 (c) ₹264 (d) ₹125
22. 22.₹312 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹156 (b) ₹216 (c) ₹24 (d) ₹96
23. 23.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 9 days (d) 25 days
24. 24.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 3 days (d) 16 days
25. 25.If 5 notebooks cost ₹90, how much do 6 notebooks cost? (a) ₹540 (b) ₹108 (c) ₹126 (d) ₹91
26. 26.If 5 notebooks cost ₹40, how much do 9 notebooks cost? (a) ₹44 (b) ₹360 (c) ₹80 (d) ₹72
27. 27.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 16 days (d) 11 days
28. 28.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 5 days (d) 4 days
29. 29.If 9 notebooks cost ₹27, how much do 10 notebooks cost? (a) ₹30 (b) ₹28 (c) ₹270 (d) ₹33
30. 30.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 9 days (d) 8 days
31. 31.If 5 pens cost ₹90, how much do 6 pens cost? (a) ₹91 (b) ₹108 (c) ₹540 (d) ₹126
32. 32.If 6 pens cost ₹126, how much do 4 pens cost? (a) ₹84 (b) ₹124 (c) ₹105 (d) ₹504
33. 33.₹320 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹96 (b) ₹160 (c) ₹224 (d) ₹32
34. 34.₹288 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹108 (b) ₹144 (c) ₹180 (d) ₹36
35. 35.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 10 days (d) 18 days
36. 36.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 31 days (b) 16 days (c) 30 days (d) 4 days
37. 37.₹279 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹248 (b) ₹279 (c) ₹31 (d) ₹249
38. 38.₹460 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹322 (b) ₹46 (c) ₹138 (d) ₹230
39. 39.₹70 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹10 (b) ₹40 (c) ₹35 (d) ₹30
40. 40.₹216 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹108 (b) ₹96 (c) ₹120 (d) ₹24

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