Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 918 · 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 notebooks cost ₹16, how much do 8 notebooks cost? (a) ₹128 (b) ₹64 (c) ₹22 (d) ₹72
2. 2.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 33 days (c) 32 days (d) 2 days
3. 3.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 15 days (c) 27 days (d) 11 days
4. 4.If 4 mangoes cost ₹64, how much do 6 mangoes cost? (a) ₹384 (b) ₹66 (c) ₹112 (d) ₹96
5. 5.₹288 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹48 (b) ₹288 (c) ₹240 (d) ₹144
6. 6.₹68 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹17 (b) ₹51 (c) ₹34 (d) ₹68
7. 7.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 10 days (d) 18 days
8. 8.₹91 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹13 (b) ₹26 (c) ₹65 (d) ₹78
9. 9.₹456 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹38 (b) ₹266 (c) ₹228 (d) ₹190
10. 10.If 2 notebooks cost ₹26, how much do 4 notebooks cost? (a) ₹28 (b) ₹104 (c) ₹52 (d) ₹65
11. 11.If 9 pens cost ₹45, how much do 10 pens cost? (a) ₹46 (b) ₹450 (c) ₹50 (d) ₹55
12. 12.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 3 days
13. 13.If 2 notebooks cost ₹44, how much do 12 notebooks cost? (a) ₹528 (b) ₹286 (c) ₹264 (d) ₹54
14. 14.If 4 kites cost ₹76, how much do 12 kites cost? (a) ₹247 (b) ₹912 (c) ₹228 (d) ₹84
15. 15.₹230 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹115 (b) ₹23 (c) ₹207 (d) ₹230
16. 16.If 9 pens cost ₹162, how much do 4 pens cost? (a) ₹648 (b) ₹90 (c) ₹72 (d) ₹157
17. 17.If 9 pens cost ₹144, how much do 10 pens cost? (a) ₹145 (b) ₹160 (c) ₹176 (d) ₹1440
18. 18.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 12 days (d) 4 days
19. 19.If 7 mangoes cost ₹56, how much do 10 mangoes cost? (a) ₹560 (b) ₹59 (c) ₹88 (d) ₹80
20. 20.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 6 days (d) 7 days
21. 21.₹154 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹77 (b) ₹22 (c) ₹66 (d) ₹88
22. 22.₹429 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹330 (b) ₹297 (c) ₹132 (d) ₹33
23. 23.If 2 pens cost ₹18, how much do 3 pens cost? (a) ₹19 (b) ₹27 (c) ₹36 (d) ₹54
24. 24.₹176 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹48 (b) ₹88 (c) ₹16 (d) ₹128
25. 25.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 9 days (d) 3 days
26. 26.If 9 notebooks cost ₹45, how much do 6 notebooks cost? (a) ₹30 (b) ₹270 (c) ₹42 (d) ₹35
27. 27.4 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
28. 28.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 16 days (d) 15 days
29. 29.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 19 days (d) 45 days
30. 30.If 7 mangoes cost ₹175, how much do 12 mangoes cost? (a) ₹325 (b) ₹300 (c) ₹2100 (d) ₹180
31. 31.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 17 days (d) 28 days
32. 32.₹221 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹68 (b) ₹17 (c) ₹170 (d) ₹153
33. 33.₹294 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹210 (b) ₹84 (c) ₹42 (d) ₹147
34. 34.₹105 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹105 (b) ₹91 (c) ₹15 (d) ₹90
35. 35.If 2 pens cost ₹18, how much do 6 pens cost? (a) ₹63 (b) ₹108 (c) ₹54 (d) ₹22
36. 36.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹13 (b) ₹65 (c) ₹91 (d) ₹78
37. 37.If 2 mangoes cost ₹14, how much do 3 mangoes cost? (a) ₹42 (b) ₹21 (c) ₹28 (d) ₹15
38. 38.₹315 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹45 (b) ₹90 (c) ₹225 (d) ₹270
39. 39.If 5 notebooks cost ₹40, how much do 8 notebooks cost? (a) ₹64 (b) ₹320 (c) ₹43 (d) ₹72
40. 40.₹294 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹126 (b) ₹168 (c) ₹147 (d) ₹42

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