Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 230 · 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 4 kites cost ₹28, how much do 2 kites cost? (a) ₹21 (b) ₹56 (c) ₹14 (d) ₹26
2. 2.₹494 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹247 (b) ₹152 (c) ₹342 (d) ₹38
3. 3.If 4 mangoes cost ₹12, how much do 6 mangoes cost? (a) ₹14 (b) ₹18 (c) ₹21 (d) ₹72
4. 4.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 7 days
5. 5.If 2 pens cost ₹14, how much do 10 pens cost? (a) ₹140 (b) ₹22 (c) ₹77 (d) ₹70
6. 6.If 2 notebooks cost ₹24, how much do 12 notebooks cost? (a) ₹156 (b) ₹34 (c) ₹288 (d) ₹144
7. 7.If 6 notebooks cost ₹138, how much do 4 notebooks cost? (a) ₹92 (b) ₹552 (c) ₹115 (d) ₹136
8. 8.₹100 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹30 (b) ₹70 (c) ₹10 (d) ₹50
9. 9.₹290 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹145 (b) ₹87 (c) ₹203 (d) ₹29
10. 10.If 4 notebooks cost ₹36, how much do 9 notebooks cost? (a) ₹81 (b) ₹90 (c) ₹41 (d) ₹324
11. 11.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 18 days (d) 12 days
12. 12.If 5 kites cost ₹95, how much do 3 kites cost? (a) ₹93 (b) ₹285 (c) ₹57 (d) ₹76
13. 13.If 4 pens cost ₹32, how much do 9 pens cost? (a) ₹80 (b) ₹72 (c) ₹37 (d) ₹288
14. 14.4 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) 3 days (d) 4 days
15. 15.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 3 days (d) 1 day
16. 16.₹280 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹35 (b) ₹280 (c) ₹140 (d) ₹245
17. 17.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 15 days (d) 9 days
18. 18.If 7 mangoes cost ₹21, how much do 11 mangoes cost? (a) ₹25 (b) ₹36 (c) ₹231 (d) ₹33
19. 19.If 3 notebooks cost ₹45, how much do 8 notebooks cost? (a) ₹50 (b) ₹135 (c) ₹120 (d) ₹360
20. 20.If 2 kites cost ₹22, how much do 5 kites cost? (a) ₹66 (b) ₹25 (c) ₹55 (d) ₹110
21. 21.If 4 pens cost ₹96, how much do 7 pens cost? (a) ₹168 (b) ₹672 (c) ₹99 (d) ₹192
22. 22.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 24 days (d) 15 days
23. 23.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 44 days (b) 5 days (c) 45 days (d) 17 days
24. 24.₹135 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹15 (b) ₹105 (c) ₹30 (d) ₹120
25. 25.₹279 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹248 (b) ₹279 (c) ₹249 (d) ₹31
26. 26.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 32 days (c) 33 days (d) 14 days
27. 27.If 6 pens cost ₹66, how much do 4 pens cost? (a) ₹55 (b) ₹64 (c) ₹264 (d) ₹44
28. 28.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 11 days
29. 29.₹108 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹12 (b) ₹108 (c) ₹96 (d) ₹54
30. 30.₹189 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹135 (b) ₹81 (c) ₹108 (d) ₹27
31. 31.If 6 notebooks cost ₹54, how much do 3 notebooks cost? (a) ₹51 (b) ₹162 (c) ₹36 (d) ₹27
32. 32.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 20 days (c) 8 days (d) 56 days
33. 33.₹165 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹135 (b) ₹45 (c) ₹120 (d) ₹15
34. 34.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 6 days (d) 10 days
35. 35.If 2 notebooks cost ₹12, how much do 4 notebooks cost? (a) ₹48 (b) ₹30 (c) ₹14 (d) ₹24
36. 36.₹264 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹144 (b) ₹132 (c) ₹24 (d) ₹120
37. 37.₹221 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹17 (b) ₹153 (c) ₹170 (d) ₹68
38. 38.₹528 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹48 (b) ₹264 (c) ₹288 (d) ₹240
39. 39.If 3 notebooks cost ₹18, how much do 4 notebooks cost? (a) ₹24 (b) ₹30 (c) ₹19 (d) ₹72
40. 40.If 2 notebooks cost ₹28, how much do 4 notebooks cost? (a) ₹30 (b) ₹112 (c) ₹56 (d) ₹70

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