Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 665 · 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.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹12 (b) ₹108 (c) ₹60 (d) ₹84
2. 2.₹252 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹28 (b) ₹126 (c) ₹140 (d) ₹112
3. 3.If 6 mangoes cost ₹30, how much do 4 mangoes cost? (a) ₹120 (b) ₹28 (c) ₹20 (d) ₹25
4. 4.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 25 days (d) 16 days
5. 5.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 44 days (c) 17 days (d) 5 days
6. 6.₹352 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹192 (b) ₹176 (c) ₹32 (d) ₹160
7. 7.If 8 kites cost ₹40, how much do 3 kites cost? (a) ₹120 (b) ₹35 (c) ₹20 (d) ₹15
8. 8.If 5 mangoes cost ₹20, how much do 6 mangoes cost? (a) ₹120 (b) ₹28 (c) ₹21 (d) ₹24
9. 9.If 4 mangoes cost ₹48, how much do 12 mangoes cost? (a) ₹56 (b) ₹156 (c) ₹576 (d) ₹144
10. 10.If 5 notebooks cost ₹15, how much do 2 notebooks cost? (a) ₹30 (b) ₹9 (c) ₹12 (d) ₹6
11. 11.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 16 days (c) 13 days (d) 1 day
12. 12.If 7 pens cost ₹21, how much do 3 pens cost? (a) ₹12 (b) ₹17 (c) ₹63 (d) ₹9
13. 13.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 25 days (d) 4 days
14. 14.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 5 days (d) 6 days
15. 15.If 7 mangoes cost ₹35, how much do 9 mangoes cost? (a) ₹50 (b) ₹315 (c) ₹37 (d) ₹45
16. 16.If 2 kites cost ₹26, how much do 7 kites cost? (a) ₹182 (b) ₹104 (c) ₹91 (d) ₹31
17. 17.₹481 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹370 (b) ₹148 (c) ₹37 (d) ₹333
18. 18.If 5 kites cost ₹20, how much do 7 kites cost? (a) ₹32 (b) ₹28 (c) ₹22 (d) ₹140
19. 19.If 3 notebooks cost ₹69, how much do 4 notebooks cost? (a) ₹92 (b) ₹276 (c) ₹70 (d) ₹115
20. 20.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 36 days (c) 15 days (d) 5 days
21. 21.If 7 pens cost ₹63, how much do 8 pens cost? (a) ₹72 (b) ₹64 (c) ₹81 (d) ₹504
22. 22.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 3 days
23. 23.If 3 pens cost ₹60, how much do 11 pens cost? (a) ₹220 (b) ₹68 (c) ₹240 (d) ₹660
24. 24.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 11 days (d) 19 days
25. 25.3 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
26. 26.If 2 notebooks cost ₹28, how much do 9 notebooks cost? (a) ₹140 (b) ₹126 (c) ₹35 (d) ₹252
27. 27.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹200 (b) ₹240 (c) ₹40 (d) ₹220
28. 28.If 7 notebooks cost ₹105, how much do 6 notebooks cost? (a) ₹630 (b) ₹90 (c) ₹104 (d) ₹105
29. 29.If 3 notebooks cost ₹27, how much do 2 notebooks cost? (a) ₹54 (b) ₹27 (c) ₹26 (d) ₹18
30. 30.₹100 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹100 (b) ₹50 (c) ₹10 (d) ₹90
31. 31.If 5 notebooks cost ₹115, how much do 4 notebooks cost? (a) ₹115 (b) ₹92 (c) ₹460 (d) ₹114
32. 32.If 4 notebooks cost ₹12, how much do 7 notebooks cost? (a) ₹21 (b) ₹24 (c) ₹84 (d) ₹15
33. 33.If 5 notebooks cost ₹25, how much do 12 notebooks cost? (a) ₹65 (b) ₹300 (c) ₹60 (d) ₹32
34. 34.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 2 days (d) 3 days
35. 35.₹528 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹264 (b) ₹48 (c) ₹192 (d) ₹336
36. 36.If 9 kites cost ₹36, how much do 12 kites cost? (a) ₹432 (b) ₹52 (c) ₹48 (d) ₹39
37. 37.₹528 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹432 (b) ₹48 (c) ₹264 (d) ₹96
38. 38.If 2 notebooks cost ₹28, how much do 3 notebooks cost? (a) ₹42 (b) ₹56 (c) ₹29 (d) ₹84
39. 39.If 3 pens cost ₹54, how much do 7 pens cost? (a) ₹126 (b) ₹58 (c) ₹378 (d) ₹144
40. 40.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 6 days (d) 9 days

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